Question

Write an equation of the ellipse centered at the origin given its vertex and co vertex ps can plz do both

Answer 1

Answer:

1. $\dfrac{x^2}{36}+\dfrac{y^2}{25}=1.$

2. $\dfrac{x^2}{16}+\dfrac{y^2}{9}=1.$

Step-by-step explanation:

The equation of the ellipse is

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

1. If the vertex of the ellipse is at point (6,0), then a=6.

If the co-vertex of the elllipse is at point (0,-5), then b=5.

The equation of the ellipse is

$\dfrac{x^2}{6^2}+\dfrac{y^2}{5^2}=1,$

$\dfrac{x^2}{36}+\dfrac{y^2}{25}=1.$

2. If the vertex of the ellipse is at point (4,0), then a=4.

If the co-vertex of the elllipse is at point (0,3), then b=3.

The equation of the ellipse is

$\dfrac{x^2}{4^2}+\dfrac{y^2}{3^2}=1,$

$\dfrac{x^2}{16}+\dfrac{y^2}{9}=1.$