Question

Write the equation of an ellipse with center (-2,-3), vertical major axis of length 14, and minor axis of

length 8.

Answer 1

Explanation:

Since we have a vertical major axis, our ellipse is vertical.

The equation of a vertical ellipse is

`\frac{(y - k) {}^(2) }{ {a}^(2) } + \frac{(x - h) {}^(2) }{ {b}^(2) } = 1`

where

(h,k) is the center

a is the semi major axis,

b is the semi minor axis

First, let plug in our center

`\frac{(y + 3) {}^(2) }{ {a}^(2) } + \frac{(x + 2) {}^(2) }{ {b}^(2) } = 1`

Semi means half, so

a is half of 14 which is 7

B is half of 8, which is 4.

`\frac{(y + 3) {}^(2) }{49} + \frac{(x + 2) {}^(2) }{16} = 1`