Write the standard form equation given the following vertices and perimeter of central rectangle

Question

Vertices (-7, 6), (-7, -12)

Perimeter of Central Rectangle = 84

Answer 1

p=2(l+w) for a rectangle

In this case, the perimeter is 84

The vertices are at (-7, 6) and (-7, -12)

They have the same x co-ordinate and different y co-ordinates, so they are 6 - -12 = 18 apart

As p = 84, 84 = 2(l+w), and 42 = l+w; l = 18, so w = 24

(6 + -12)/2 = -3

Our center is at (-7, -3)

Then, the standard form of the ellipse is (y - -3)²/(1/2l)² - (x - -7)²/(1/2w)² = 1

(y + 3)²/81 - (x +7)²/144= 1