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If the vertices of a hyperbola be at (-2...

If the vertices of a hyperbola be at (-2, 0) and (2, 0) and one of its foci be at (-3, 0), then which one of the following points does not lie on this hyperbola ?

A

`(2sqrt(6),5)`

B

`(6,5sqrt(2))`

C

`(4, sqrt(15))`

D

`(-6, 2sqrt(10))`

Text Solution

Verified by Experts

The verticles of hyperbola are given as `(pm 2, 0)` and one of its foci is at (-3, 0).
` therefore (a, 0) =(2, 0) and (-a e, 0),=(-3,0)`
On comparing x-coordinates both sides, we get
`rArr a=2 and -ae = -3`
`rArr 2e=3 rArr e=(3)/(2)`
Also, `(9)/(4)=1+(b^(2))/(4) rArr b^(2)=5 " " [ therefore e^(2) =1+(b^(2))/(a^(2))]`
So, equation of the hyperbola is
`(x^(2))/(4) -(y^(2))/(5)=1 " ...(i)" `
The point `(6, 5sqrt(2))` from the given options does not satisfy the above equations of hyperbola.
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