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The equation of the tangent to the hyper...

The equation of the tangent to the hyperbola `3x^(2) - 8y^(2) = 24` and perpendicular to the line `3x -2y = 4` is

A

`3x+2y pm sqrt(5)=0`

B

`2x+3y pm sqrt(7)=0`

C

`2x+3y pm 2 =0 `

D

`2x+3y pm sqrt(5)=0`

Text Solution

Verified by Experts

The correct Answer is:
D
A line perpendicular to given line
`2x+3y=lambda`
`m= -(2)/(3)" " c=(lambda)/(3)`
Condition of tangency
`c^(2)=a^(2)m^(2)-b^(2)" " a^(2)=8`
`" " b^(2)=3`
`(lambda^(2))/(9) =8(4)/(9) -3`
`lambda^(2)=32-27=5`
`lambda = pm sqrt(5)`
Tangents are `2x+3y pm sqrt(5)=0`
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