Find the standard form of the equation of the ellipse centered at the origin with minor axis of the length 6 and vertex located at (0,-9)

Question

Find the standard form of the equation of the ellipse centered at the origin with minor axis of the length 6 and vertex located at (0,-9)

Answer 1

The standard equation of an ellipse with its center in the origin is (x²/a²)+(y²/b²)=1 if the major axis is horizontal or (x²/b²)+(y²/a²)=1 if the major axis is vertical. In this problem the length of the minor axis is 6. Since there is one vertex located at (0,-9), the other must be at (0,9) So the length of this axis is 18. You this must be the major axis, this would be the correct equation:

(x²/b²)+(y²/a²)=1

a is half the distance of the major axis, which is 9.

b is half the distance of the minor axis, which is 3.

Plugging these in:

(x²/3²)+(y²/9²)=1 Simplify

(x²/9)+(y²/81)=1