Question

Find the equation of the ellipse with the following properties.

Answer 1

The equation of an ellipse where the major axis 2a is greater than the minor 2b
 (x-h)²/a² + (y-k)²/b² =1.
When 2b>2a , then the equation becomes (y-h)²/b² + (x-k)²/a² =1
In our example a = 4 and b = 9. Moreover h=0 and k=0 because the center is on the origin, so the equation becomes:
y²/b² + x²/a² = y²/81 + x²/16 = 1

Answer 2

Check the picture below

so.. hmm notice the center h,k and the major and minor axis components, thus just plug them in.