What is the equation of a vertical ellipse with a major axis= 20 and a minor axis = 14?

Question

asked Jan 14, 2021 233k views

1 Answer

Fitch · Answer 1 · 2021-01-18T19:53:15+0000

$\bold{\text{Answer: b.}\quad (y^2)/(100)+(x^2)/(49)=1}$

Explanation:

The ellipse is vertical so y has the biggest radius.

Major axis (y) = 20 so the y-radius is 20/2 = 10

Minor axis (x) = 14 so the x-radius is 14/2 = 7

The equation of an ellipse is:
((x-h)^2)/(a^2)+((y-k)^2)/(b^2)=1 where

Given: a = 7, b = 10

Assume: (h, k) = (0, 0)

$((x-0)^2)/(7^2)+((y-0)^2)/(10^2)=1\\\\\\(x^2)/(49)+(y^2)/(100)=1\\\\\\\longrightarrow (y^2)/(100)+(x^2)/(49)=1$