Question

Find the equation of the ellipse with the following properties.

Answer 1

Answer:

The equation of ellipse is $\frac{x^2}{25}+\frac{y^2}{9}=1$.

Step-by-step explanation:

The center of ellipse is origin because the ellipse has foci at (4, 0) and (-4, 0); y-intercepts (0, 3) and (0, -3).

The general equation of an ellipse is

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

Where, a is major axis and b is minor.

The y-intercepts are (0, 3) and (0, -3). So, the value of b is 3.

The foci of ellipse is $(\pm c,0)$.The relation between foci and major, minor axis is

$c^2=a^2-b^2$

$(4)^2=a^2-(3)^2$

$16=a^2-9$

$a^2=25$

$a=5$

The equation of ellipse is

$\frac{x^2}{5^2}+\frac{y^2}{3^2}=1$

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