Question

Find an equation in standard form for the ellipse with the vertical major axis of length 6 and minor axis of length 4

Answer 1

x^2/4 +y^2/9 = 1

Explanation:

The standard form is ...

(x -h)^2/a^2 +(y -k)^2/b^2 = 1

for an ellipse centered at (h, k) with semi-axis measures "a" and "b". The largest of "a" or "b" is the semi-major axis; the smaller, the semi-minor axis.

Here, the major axis is vertical, so b > a.

Since the center is not given, we assume it is the origin: h = k = 0. The semi-axes are a=2, b=3, so the equation is ...

x^2/4 +y^2/9 = 1