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 ((x+4)^2)/(81)+((y-5)^2)/(25)=1}`

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:
`((x-h)^2)/(a^2)+((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:

`((x-(-4))^2)/(9^2)+((y-5)^2)/(5^2)=1`

Simplify to get:

`((x+4)^2)/(81)+((y-5)^2)/(25)=1`

Answer 2

See the attached picture