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Equation of normal to hyperbola x^(2)-y^...

Equation of normal to hyperbola `x^(2)-y^(2) = 2`
Passing through (6, 0)

A

`(x)/(3) pm (y)/(sqrt(7)) = 2`

B

`(x)/(3) pm (y)/(sqrt(5)) = 2`

C

`(x)/(3) pm (y)/(7) = 2`

D

`(x)/(3) pm (y)/(5) = 2`

Text Solution

Verified by Experts

The correct Answer is:
A
`(a^(2)x)/(x_(1)) + (b^(2)y)/(y_(1)) = a^(2) + b^(2)`
`(x)/(x_(1)) + (y)/(y_(1)) = 2` Passinf through (6,0)
`(6)/(x_(1)) + 0 = 2 rArr x_(1) = 3`
`x_(1)^(2) - y_(1)^(2) = 2`
`9 - y_(1)^(2) = 2 rArr y_(1) = pm sqrt(7)`
So Eq. of Normal is `(x)/(3) pm (y)/(sqrt(7)) = 2`
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