Question

The equation of the ellipse whose vertices are `(+- 5, 0)` and foci at `(+-4, 0)` is
A. `(x^(2))/25+(y^(2))/9=1`
B. `(x^(2))/16+(y^(2))/9=1`
C. `(x^(2))/25+(y^(2))/16=1`
D. `(x^(2))/9+(y^(2))/25=1`

Answer 1

Correct Answer - A
Given,
vertices, (5, 0) and (-5, 0)
foci (4, 0) and (-4, 0)

`"i.e., ae = 4"`
`rArre=4/a=4/5`
`"We know,"b^(2)=a^(2)(1-e^(2))`
`=5^(2)(1-(4/5)^(2))`
`25((25-16)/25)=9`
`:.a^(2)=25, b^(2)=9`
`"Equation of ellipse is "x^(2)/15+y^(2)/9=1`