(x29)+(y225)=1

Remove parentheses.

x29+y225=1

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.

(x-h)2b2+(y-k)2a2=1

Match the values in this ellipse to those of the standard form. The variable a represents the radius of the major axis of the ellipse, b represents the radius of the minor axis of the ellipse, h represents the x-offset from the origin, and k represents the y-offset from the origin.

a=5

b=3

k=0

h=0

The center of an ellipse follows the form of (h,k). Substitute in the values of h and k.

(0,0)

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

a2-b2

Substitute the values of a and b in the formula.

(5)2-(3)2

Simplify.

Raise 5 to the power of 2.

25-(3)2

Raise 3 to the power of 2.

25-1⋅9

Multiply -1 by 9.

25-9

Subtract 9 from 25.

16

Rewrite 16 as 42.

42

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

4

4

4

The first vertex of an ellipse can be found by adding a to k.

(h,k+a)

Substitute the known values of h, a, and k into the formula.

(0,0+5)

Simplify.

(0,5)

The second vertex of an ellipse can be found by subtracting a from k.

(h,k-a)

Substitute the known values of h, a, and k into the formula.

(0,0-(5))

Simplify.

(0,-5)

Ellipses have two vertices.

Vertex1: (0,5)

Vertex2: (0,-5)

Vertex1: (0,5)

Vertex2: (0,-5)

The first focus of an ellipse can be found by adding c to k.

(h,k+c)

Substitute the known values of h, c, and k into the formula.

(0,0+4)

Simplify.

(0,4)

The first focus of an ellipse can be found by subtracting c from k.

(h,k-c)

Substitute the known values of h, c, and k into the formula.

(0,0-(4))

Simplify.

(0,-4)

Ellipses have two foci.

Focus1: (0,4)

Focus2: (0,-4)

Focus1: (0,4)

Focus2: (0,-4)

Find the eccentricity by using the following formula.

a2-b2a

Substitute the values of a and b into the formula.

(5)2-(3)25

Simplify the numerator.

Raise 5 to the power of 2.

25-(3)25

Raise 3 to the power of 2.

25-1⋅95

Multiply -1 by 9.

25-95

Subtract 9 from 25.

165

Rewrite 16 as 42.

425

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

45

45

45

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

Center: (0,0)

Vertex1: (0,5)

Vertex2: (0,-5)

Focus1: (0,4)

Focus2: (0,-4)

Eccentricity: 45

Graph ((x^2)/9)+((y^2)/25)=1