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From the external point T(0, 3), tangents are drawn to the hyperbola 4x² - y² = 36 touching it at P and Q. Find the area (in square units) of triangle PTQ.
- 45*sqrt(5)
- 54*sqrt(3)
- 60*sqrt(3)
- 36*sqrt(5)
Correct answer: 45*sqrt(5)
Solution
The chord of contact from T(0,3) gives line y = -12; finding its intersections with the hyperbola and the distance from T leads to area 45*sqrt(5).
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