Question

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

Answer 1

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

Step-by-step 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:   $\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1$   where

• (h, k) is the center of the ellipse
• a is the x-radius
• b is the y-radius

Given: a = 7, b = 10

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

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