How do I find the equation of an ellipse given a minor axis of twelve and x-intercepts of (9,0) and (-9,0)

Question

For my final exam, I was given the above practice problem. I set up the equation using the given information but that means I would have to find a, h, and k. How would I do this? Am I overthinking this? Because the next problems see to be less extensive.

Answer 1

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

 

Given x-intercepts of (9,0) and (-9,0), h =(-9+9)/2 =0, k = (0+0)/2 = 0

Major = 2a = [9 -(-9)/2] = 18 ⇒ a = 9

Minor = 2b =12 ⇒ b = 6

 

The equation for the ellipse x²/9² + y²/6² = 1.

 

May be you are overthinking.

If the center is not (0, 0) , it will be (0, k), and more information will be needed to solve for a and k before you can write the equation.