Question

Write an equation of the ellipse centered at the origin given its vertex and co vertex Can you please do both

Answer 1

Answer:

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

2. $\dfrac{x^2}{121}+\dfrac{y^2}{100}=1.$

Step-by-step explanation:

The equation of the ellipse is

$\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1\ (a>b)$

or

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

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

If the co-vertex of the elllipse is at point (-1,0), then a=1.

The equation of the ellipse is

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

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

This ellipse has foci on y-axis.

2. If the vertex of the ellipse is at point (-11,0), then a=11.

If the co-vertex of the elllipse is at point (0,10), then b=10.

The equation of the ellipse is

$\dfrac{x^2}{11^2}+\dfrac{y^2}{10^2}=1,$

$\dfrac{x^2}{121}+\dfrac{y^2}{100}=1.$