Add <math><mstyle displaystyle="true"><mn>156</mn></mstyle></math> to both sides of the equation.

Complete the square for <math><mstyle displaystyle="true"><mn>25</mn><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>-</mo><mn>100</mn><mi>x</mi></mstyle></math> .

Use the form <math><mstyle displaystyle="true"><mi>a</mi><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mi>b</mi><mi>x</mi><mo>+</mo><mi>c</mi></mstyle></math> , to find the values of <math><mstyle displaystyle="true"><mi>a</mi></mstyle></math> , <math><mstyle displaystyle="true"><mi>b</mi></mstyle></math> , and <math><mstyle displaystyle="true"><mi>c</mi></mstyle></math> .

Consider the vertex form of a parabola.

Substitute the values of <math><mstyle displaystyle="true"><mi>a</mi></mstyle></math> and <math><mstyle displaystyle="true"><mi>b</mi></mstyle></math> into the formula <math><mstyle displaystyle="true"><mi>d</mi><mo>=</mo><mfrac><mrow><mi>b</mi></mrow><mrow><mn>2</mn><mi>a</mi></mrow></mfrac></mstyle></math> .

Simplify the right side.

Cancel the common factor of <math><mstyle displaystyle="true"><mn>100</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>100</mn></mstyle></math> .

Cancel the common factors.

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>2</mn><mo>⋅</mo><mn>25</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Cancel the common factor of <math><mstyle displaystyle="true"><mn>50</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>25</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>25</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>50</mn></mstyle></math> .

Cancel the common factors.

Factor <math><mstyle displaystyle="true"><mn>25</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>25</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Divide <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Find the value of <math><mstyle displaystyle="true"><mi>e</mi></mstyle></math> using the formula <math><mstyle displaystyle="true"><mi>e</mi><mo>=</mo><mi>c</mi><mo>-</mo><mfrac><mrow><msup><mrow><mi>b</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><mn>4</mn><mi>a</mi></mrow></mfrac></mstyle></math> .

Simplify each term.

Raise <math><mstyle displaystyle="true"><mo>-</mo><mn>100</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>25</mn></mstyle></math> .

Divide <math><mstyle displaystyle="true"><mn>10000</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>100</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>100</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>100</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Substitute the values of <math><mstyle displaystyle="true"><mi>a</mi></mstyle></math> , <math><mstyle displaystyle="true"><mi>d</mi></mstyle></math> , and <math><mstyle displaystyle="true"><mi>e</mi></mstyle></math> into the vertex form <math><mstyle displaystyle="true"><mi>a</mi><msup><mrow><mo>(</mo><mi>x</mi><mo>+</mo><mi>d</mi><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mi>e</mi></mstyle></math> .

Substitute <math><mstyle displaystyle="true"><mn>25</mn><msup><mrow><mo>(</mo><mi>x</mi><mo>-</mo><mn>2</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>-</mo><mn>100</mn></mstyle></math> for <math><mstyle displaystyle="true"><mn>25</mn><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>-</mo><mn>100</mn><mi>x</mi></mstyle></math> in the equation <math><mstyle displaystyle="true"><mn>25</mn><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mn>16</mn><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>-</mo><mn>100</mn><mi>x</mi><mo>+</mo><mn>96</mn><mi>y</mi><mo>=</mo><mn>156</mn></mstyle></math> .

Move <math><mstyle displaystyle="true"><mo>-</mo><mn>100</mn></mstyle></math> to the right side of the equation by adding <math><mstyle displaystyle="true"><mn>100</mn></mstyle></math> to both sides.

Complete the square for <math><mstyle displaystyle="true"><mn>16</mn><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mn>96</mn><mi>y</mi></mstyle></math> .

Use the form <math><mstyle displaystyle="true"><mi>a</mi><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mi>b</mi><mi>x</mi><mo>+</mo><mi>c</mi></mstyle></math> , to find the values of <math><mstyle displaystyle="true"><mi>a</mi></mstyle></math> , <math><mstyle displaystyle="true"><mi>b</mi></mstyle></math> , and <math><mstyle displaystyle="true"><mi>c</mi></mstyle></math> .

Consider the vertex form of a parabola.

Substitute the values of <math><mstyle displaystyle="true"><mi>a</mi></mstyle></math> and <math><mstyle displaystyle="true"><mi>b</mi></mstyle></math> into the formula <math><mstyle displaystyle="true"><mi>d</mi><mo>=</mo><mfrac><mrow><mi>b</mi></mrow><mrow><mn>2</mn><mi>a</mi></mrow></mfrac></mstyle></math> .

Simplify the right side.

Cancel the common factor of <math><mstyle displaystyle="true"><mn>96</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>96</mn></mstyle></math> .

Cancel the common factors.

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>2</mn><mo>⋅</mo><mn>16</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Cancel the common factor of <math><mstyle displaystyle="true"><mn>48</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>16</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>16</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>48</mn></mstyle></math> .

Cancel the common factors.

Factor <math><mstyle displaystyle="true"><mn>16</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>16</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Divide <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Find the value of <math><mstyle displaystyle="true"><mi>e</mi></mstyle></math> using the formula <math><mstyle displaystyle="true"><mi>e</mi><mo>=</mo><mi>c</mi><mo>-</mo><mfrac><mrow><msup><mrow><mi>b</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><mn>4</mn><mi>a</mi></mrow></mfrac></mstyle></math> .

Simplify each term.

Raise <math><mstyle displaystyle="true"><mn>96</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>16</mn></mstyle></math> .

Divide <math><mstyle displaystyle="true"><mn>9216</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>64</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>144</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>144</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Substitute the values of <math><mstyle displaystyle="true"><mi>a</mi></mstyle></math> , <math><mstyle displaystyle="true"><mi>d</mi></mstyle></math> , and <math><mstyle displaystyle="true"><mi>e</mi></mstyle></math> into the vertex form <math><mstyle displaystyle="true"><mi>a</mi><msup><mrow><mo>(</mo><mi>x</mi><mo>+</mo><mi>d</mi><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mi>e</mi></mstyle></math> .

Substitute <math><mstyle displaystyle="true"><mn>16</mn><msup><mrow><mo>(</mo><mi>y</mi><mo>+</mo><mn>3</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>-</mo><mn>144</mn></mstyle></math> for <math><mstyle displaystyle="true"><mn>16</mn><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mn>96</mn><mi>y</mi></mstyle></math> in the equation <math><mstyle displaystyle="true"><mn>25</mn><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mn>16</mn><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>-</mo><mn>100</mn><mi>x</mi><mo>+</mo><mn>96</mn><mi>y</mi><mo>=</mo><mn>156</mn></mstyle></math> .

Move <math><mstyle displaystyle="true"><mo>-</mo><mn>144</mn></mstyle></math> to the right side of the equation by adding <math><mstyle displaystyle="true"><mn>144</mn></mstyle></math> to both sides.

Simplify <math><mstyle displaystyle="true"><mn>156</mn><mo>+</mo><mn>100</mn><mo>+</mo><mn>144</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>156</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>100</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>256</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>144</mn></mstyle></math> .

Divide each term by <math><mstyle displaystyle="true"><mn>400</mn></mstyle></math> to make the right side equal to one.

Simplify each term in the equation in order to set the right side equal to <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> . The standard form of an ellipse or hyperbola requires the right side of the equation be <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

This is the form of an ellipse. Use this form to determine the values used to find the center along with the major and minor axis of the ellipse.

Match the values in this ellipse to those of the standard form. The variable <math><mstyle displaystyle="true"><mi>a</mi></mstyle></math> represents the radius of the major axis of the ellipse, <math><mstyle displaystyle="true"><mi>b</mi></mstyle></math> represents the radius of the minor axis of the ellipse, <math><mstyle displaystyle="true"><mi>h</mi></mstyle></math> represents the x-offset from the origin, and <math><mstyle displaystyle="true"><mi>k</mi></mstyle></math> represents the y-offset from the origin.

The center of an ellipse follows the form of <math><mstyle displaystyle="true"><mrow><mo>(</mo><mi>h</mi><mo>,</mo><mi>k</mi><mo>)</mo></mrow></mstyle></math> . Substitute in the values of <math><mstyle displaystyle="true"><mi>h</mi></mstyle></math> and <math><mstyle displaystyle="true"><mi>k</mi></mstyle></math> .

Find the distance from the center to a focus of the ellipse by using the following formula.

Substitute the values of <math><mstyle displaystyle="true"><mi>a</mi></mstyle></math> and <math><mstyle displaystyle="true"><mi>b</mi></mstyle></math> in the formula.

Simplify.

Raise <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>16</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>16</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>25</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>9</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Pull terms out from under the radical, assuming positive real numbers.

The first vertex of an ellipse can be found by adding <math><mstyle displaystyle="true"><mi>a</mi></mstyle></math> to <math><mstyle displaystyle="true"><mi>k</mi></mstyle></math> .

Substitute the known values of <math><mstyle displaystyle="true"><mi>h</mi></mstyle></math> , <math><mstyle displaystyle="true"><mi>a</mi></mstyle></math> , and <math><mstyle displaystyle="true"><mi>k</mi></mstyle></math> into the formula.

Simplify.

The second vertex of an ellipse can be found by subtracting <math><mstyle displaystyle="true"><mi>a</mi></mstyle></math> from <math><mstyle displaystyle="true"><mi>k</mi></mstyle></math> .

Substitute the known values of <math><mstyle displaystyle="true"><mi>h</mi></mstyle></math> , <math><mstyle displaystyle="true"><mi>a</mi></mstyle></math> , and <math><mstyle displaystyle="true"><mi>k</mi></mstyle></math> into the formula.

Simplify.

Ellipses have two vertices.

The first focus of an ellipse can be found by adding <math><mstyle displaystyle="true"><mi>c</mi></mstyle></math> to <math><mstyle displaystyle="true"><mi>k</mi></mstyle></math> .

Substitute the known values of <math><mstyle displaystyle="true"><mi>h</mi></mstyle></math> , <math><mstyle displaystyle="true"><mi>c</mi></mstyle></math> , and <math><mstyle displaystyle="true"><mi>k</mi></mstyle></math> into the formula.

Simplify.

The first focus of an ellipse can be found by subtracting <math><mstyle displaystyle="true"><mi>c</mi></mstyle></math> from <math><mstyle displaystyle="true"><mi>k</mi></mstyle></math> .

Substitute the known values of <math><mstyle displaystyle="true"><mi>h</mi></mstyle></math> , <math><mstyle displaystyle="true"><mi>c</mi></mstyle></math> , and <math><mstyle displaystyle="true"><mi>k</mi></mstyle></math> into the formula.

Simplify.

Ellipses have two foci.

Find the eccentricity by using the following formula.

Substitute the values of <math><mstyle displaystyle="true"><mi>a</mi></mstyle></math> and <math><mstyle displaystyle="true"><mi>b</mi></mstyle></math> into the formula.

Simplify the numerator.

Raise <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>16</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>16</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>25</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>9</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Pull terms out from under the radical, assuming positive real numbers.

These values represent the important values for graphing and analyzing an ellipse.

Center: <math><mstyle displaystyle="true"><mrow><mo>(</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>)</mo></mrow></mstyle></math>

Eccentricity: <math><mstyle displaystyle="true"><mfrac><mrow><mn>3</mn></mrow><mrow><mn>5</mn></mrow></mfrac></mstyle></math>

Do you know how to Graph 25x^2+16y^2-100x+96y-156=0? If not, you can write to our math experts in our application. The best solution for your task you can find above on this page.

Name | seven hundred thirty-five million six hundred twenty-six thousand four hundred sixty |
---|

- 735626460 has 64 divisors, whose sum is
**2649884544** - The reverse of 735626460 is
**064626537** - Previous prime number is
**5171**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 39
- Digital Root 3

Name | seven hundred thirty-seven million one hundred eighty-one thousand seven hundred eighty-six |
---|

- 737181786 has 16 divisors, whose sum is
**1113825600** - The reverse of 737181786 is
**687181737** - Previous prime number is
**179**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 48
- Digital Root 3

Name | one hundred seventy-six million two hundred twenty-six thousand seven hundred fourteen |
---|

- 176226714 has 8 divisors, whose sum is
**293711220** - The reverse of 176226714 is
**417622671** - Previous prime number is
**9**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 36
- Digital Root 9