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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