An ellipse has a center at the origin, a vertex along the minor axis at (0,-8), and a focus at (15,0). Which equation represents this ellipse?

We have been given that an ellipse has a center at the origin, a vertex along the minor axis at (0,-8), and a focus at (15,0). We are asked to find the equation for the ellipse.

The standard from an ellipse centered at origin with major axes at x-axis is , where

a = Horizontal radius,  

b = Vertical radius.

Since focus is at x-axis, so our ellipse will be a major horizontal axis.

Horizontal radius will be equal to distance from origin to point (15,0) that is

The vertical radius would be distance from origin to point (0,-8) that is:

Upon substituting values of a and b in above equation, we will get:

Therefore, our required equation would be .

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