Question

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

Answer 1

1.
`(x^2)/(1)+(y^2)/(4)=1.`

2.
`(x^2)/(121)+(y^2)/(100)=1.`

Explanation:

The equation of the ellipse is

`(x^2)/(a^2)+(y^2)/(b^2)=1\ (a>b)`

or

`(x^2)/(b^2)+(y^2)/(a^2)=1\ (a<b).`

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

`(x^2)/(1^2)+(y^2)/(2^2)=1,`

`(x^2)/(1)+(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

`(x^2)/(11^2)+(y^2)/(10^2)=1,`

`(x^2)/(121)+(y^2)/(100)=1.`