Answer to Question #163334 in Analytic Geometry for sara

Question

Find an equation of the ellipse that has a center(0,5), a minor axis of length 8, and a vertex at  (0,-1).

Answer 1

Solution.

Write equation of the ellipse

$$\frac{(x-x_0)^2}{a^2}+\frac{(y-y_0)^2}{b^2}=1,$$

where $(x_0;y_0)$ is a center,

$2a$ i $2b$ - are axis.

Since the distance from the center of the ellipse to its vertex is 6, then $b=6.$ The minor axis is 8, so $a=8:2=4.$

We will get

$$\frac{x^2}{4^2}+\frac{(y-5)^2}{6^2}=1,$$

This is the equation of the ellipse. Let's simplify it:

$$9x^2+4y^2-40y-44=0.$$

Answer.

$$9x^2+4y^2-40y-44=0.$$