Question

What is the equation of the ellipse with foci at (5, 0), (-5, 0) and vertices (9, 0), (-9, 0)?

Answer 1

Answer:
`(x^2)/(81)+(y^2)/(56)=1`

Explanation:

General equation of ellipse :
`(x^2)/(a^2)+(y^2)/(b^2)`

Given: Vertices of ellipse : (± 9,0)

Since the vertices are of the form (± a, 0).

i.e. a=9

Thus, the major axis is along x-axis.

Also, foci of the ellipse = (±5,0)

Since, foci is of the form (± c,0), i.e. c=5

Since

`c^2=a^2-b^2\\\\\Rightarrow\ 5^2= 9^2-b^2\\\\\Rightarrow\ b^2=81-25\\\\\Rightarrow\ b^2=56`

Equation of ellipse :

`(x^2)/(9^2)+(y^2)/(56)=1\\\\\Rightarrow\ (x^2)/(81)+(y^2)/(56)=1`

Hence, the required equation :
`(x^2)/(81)+(y^2)/(56)=1`