Question

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

Answer 1

1.
`(x^2)/(36)+(y^2)/(25)=1.`

2.
`(x^2)/(16)+(y^2)/(9)=1.`

Explanation:

The equation of the ellipse is

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

`(x^2)/(6^2)+(y^2)/(5^2)=1,`

`(x^2)/(36)+(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

`(x^2)/(4^2)+(y^2)/(3^2)=1,`

`(x^2)/(16)+(y^2)/(9)=1.`