An ellipse has a center at the origin, a vertex along the major axis at (13, 0), and a focus at (12, 0). what is the equation of the ellipse?

 The equation of the ellipse is

Step-by-step explanation:  We are given to find the equation of an ellipse that has a center at the origin, a vertex along the major axis at (13, 0) and a focus at (12, 0).

Since the focus lies on the X-axis, so the standard equation of an ellipse with major axis as X-axis is given by

According to given information, we have

a vertex along the major axis, (a, 0) = (13, 0)  

⇒ length of the major axis, a = 13,

co-ordinates of focus, (c, 0) = (12, 0)

⇒ c = 12.

We know that

Therefore,

Thus, from equation (i), we get

The equation of the ellipse is

20

step-by-step explanation: