# Graph 25x^2+16y^2-100x+96y-156=0

Graph 25x^2+16y^2-100x+96y-156=0
Find the standard form of the ellipse.
Add to both sides of the equation.
Complete the square for .
Use the form , to find the values of , , and .
Consider the vertex form of a parabola.
Substitute the values of and into the formula .
Simplify the right side.
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by .
Multiply by .
Find the value of using the formula .
Simplify each term.
Raise to the power of .
Multiply by .
Divide by .
Multiply by .
Subtract from .
Substitute the values of , , and into the vertex form .
Substitute for in the equation .
Move to the right side of the equation by adding to both sides.
Complete the square for .
Use the form , to find the values of , , and .
Consider the vertex form of a parabola.
Substitute the values of and into the formula .
Simplify the right side.
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by .
Find the value of using the formula .
Simplify each term.
Raise to the power of .
Multiply by .
Divide by .
Multiply by .
Subtract from .
Substitute the values of , , and into the vertex form .
Substitute for in the equation .
Move to the right side of the equation by adding to both sides.
Simplify .
Add and .
Add and .
Divide each term by to make the right side equal to one.
Simplify each term in the equation in order to set the right side equal to . The standard form of an ellipse or hyperbola requires the right side of the equation be .
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 represents the radius of the major axis of the ellipse, represents the radius of the minor axis of the ellipse, represents the x-offset from the origin, and represents the y-offset from the origin.
The center of an ellipse follows the form of . Substitute in the values of and .
Find , the distance from the center to a focus.
Find the distance from the center to a focus of the ellipse by using the following formula.
Substitute the values of and in the formula.
Simplify.
Raise to the power of .
Raise to the power of .
Multiply by .
Subtract from .
Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
Find the vertices.
The first vertex of an ellipse can be found by adding to .
Substitute the known values of , , and into the formula.
Simplify.
The second vertex of an ellipse can be found by subtracting from .
Substitute the known values of , , and into the formula.
Simplify.
Ellipses have two vertices.
:
:
:
:
Find the foci.
The first focus of an ellipse can be found by adding to .
Substitute the known values of , , and into the formula.
Simplify.
The first focus of an ellipse can be found by subtracting from .
Substitute the known values of , , and into the formula.
Simplify.
Ellipses have two foci.
:
:
:
:
Find the eccentricity.
Find the eccentricity by using the following formula.
Substitute the values of and into the formula.
Simplify the numerator.
Raise to the power of .
Raise to the power of .
Multiply by .
Subtract from .
Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
These values represent the important values for graphing and analyzing an ellipse.
Center:
:
:
:
:
Eccentricity:
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### Name

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

### Interesting facts

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

### Basic properties

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

### Name

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

### Interesting facts

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

### Basic properties

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

### Name

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

### Interesting facts

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

### Basic properties

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