Question

An ellipse has a vertex at (5,0), a co-vertex at (0, -3), and a center at the origin. Which is the equation of the ellipse in standard form?

Answer 1

Answer:

$\frac{x^2}{25}+\frac{y^2}{9}=1$

Step-by-step explanation:

$\frac{(x-h)^2}{a^2}+\frac[(y-k)^2}{b^2}=1$

her center $(h,k)$, and $a$ is the horizontal radius, and $b$ is the vertical radius.

So the center is $(h,k)=(0,0)$.

$a=5$ because (5,0) has a distance of 5 from (0,0).

$b=3$ because (0,-3) has a distance of 3 from (0,0).

So the equation is:

$\frac{(x-0)^2}{5^2}+\frac{(y-0)^2}{3^2}=1$

Simplifying a bit:

$\frac{x^2}{25}+\frac{y^2}{9}=1$