Question

write the equation of a horizontal ellipse with a major axis of 18, and minor axis of 10, and a center at (-4, 5).​

Answer 1

$\bold{\text{Answer:}\quad \dfrac{(x+4)^2}{81}+\dfrac{(y-5)^2}{25}=1}$

Step-by-step explanation:

A "horizontal" ellipse means that the x-radius is bigger than the y-radius.  Thus, x is the major axis and y is the minor axis.

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 radius on the x-axis
• b is the radius on the y-axis

It is given that the center is at (-4, 5) --> h = -4, k = 5

It is given that the major axis has a length of 18 --> x-radius = 9

It is given that the minor axis has a length of 10 --> y-radius = 5

Input those values into the equation of an ellipse to get:

$\dfrac{(x-(-4))^2}{9^2}+\dfrac{(y-5)^2}{5^2}=1$

Simplify to get:

$\dfrac{(x+4)^2}{81}+\dfrac{(y-5)^2}{25}=1$

Answer 2

See the attached picture