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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

`45sqrt(5)`

B

`54 sqrt(3)`

C

`60sqrt(3)`

D

`36sqrt(5)`

Text Solution

Verified by Experts

Tangents are drawn to the hyperbola `4x^(2)-y^(2)=36` at the point P and Q.
Tangent intersects at point `T(0, 3)`

Clearly, PQ is chord of contact.
` therefore " Equation of PQ is " -3y=36`
` rArr y= -12`
Solving the curve `4x^(2)-y^(2)=36 and y= -12`,
we get `x= pm 3sqrt(5)`
Area of `triangle PQT=(1)/(2) xx PQ xx ST =(1)/(2) (6sqrt(5)xx 15)=45sqrt(5)`
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