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Tangents are drawn to the hyperbola 4x^2...

Tangents are drawn to the hyperbola `4x^2-y^2=36` at the points P and Q. If these tangents intersect at the point T(0,3) then the area (in sq units) of `triangle PTQ` is

A

`36sqrt5`

B

`45sqrt5`

C

`54sqrt3`

D

`60sqrt3`

Text Solution

Verified by Experts

The correct Answer is:
B
In the figure, PQ is chord of cantact w.r.t. point T(0,3).
Equation of PQ is
`4(0xx x)-(y-xx3)" or "y=-12`
Solving line PQ with the hyperbola, we get
`4x^(2)-144=36`
`rArr" "4x^(2)=180`
`rArr" "x^(2)=45`
`rArr" "x=pm3 sqrt5`
`therefore" "P(-3sqrt5,-12),Q(sqrt5,-12)`

`therefore" Area of triangle TPQ"=(1)/(2)xxPQxxTM`
`=(1)/(2)xx6sqrt5xx15=45sqrt5" sq. units"`
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