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>3</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>9</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>9</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>25</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>16</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>4</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>h</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>h</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>h</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 second vertex of an ellipse can be found by subtracting <math><mstyle displaystyle="true"><mi>c</mi></mstyle></math> from <math><mstyle displaystyle="true"><mi>h</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>3</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>9</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>9</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>25</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>16</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>4</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><mo>-</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow></mstyle></math>

Eccentricity: <math><mstyle displaystyle="true"><mfrac><mrow><mn>4</mn></mrow><mrow><mn>5</mn></mrow></mfrac></mstyle></math>

Do you know how to Graph ((x+1)^2)/25+((y-2)^2)/9=1? 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 | one billion six hundred thirty million three hundred seventy-seven thousand eight hundred ninety-nine |
---|

- 1630377899 has 8 divisors, whose sum is
**1667980512** - The reverse of 1630377899 is
**9987730361** - Previous prime number is
**71**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 53
- Digital Root 8

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

- 2120677031 has 8 divisors, whose sum is
**2314946304** - The reverse of 2120677031 is
**1307760212** - Previous prime number is
**1583**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 29
- Digital Root 2

Name | one hundred sixty-one million seven hundred forty-one thousand three hundred fifty-seven |
---|

- 161741357 has 8 divisors, whose sum is
**163160640** - The reverse of 161741357 is
**753147161** - Previous prime number is
**179**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 35
- Digital Root 8