Question

Write an equation in standard form of an ellipse that is 50 units high and 40 units wide. The center of the ellipse is (0,0).

Answer 1

Answer:

$\frac{x^2}{400}+\frac{y^2}{625}=1$

Step-by-step explanation:

The equation of an ellipse that has its center at the origin is given by the formula:

$\frac{x^2}{b^2}+\frac{y^2}{a^2}=1$

The given ellipse is 50 units high.

This means that length of the major axis is 50.

$2a=50$

$2\implies a=25$

The ellipse is 40 units wide.

$2b=40$

$\implies b=20$

We substitute these values into the formula to get:

$\frac{x^2}{20^2}+\frac{y^2}{25^2}=1$

$\frac{x^2}{400}+\frac{y^2}{625}=1$