Question

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

Answer 1

Step-by-step 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.

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