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Tangents are drawn to the hyperbola 4 x^2 - y^2=36 at point P and Q.If these tangents intersect at point T(0,3) find area of triangle formed

Tangents are drawn to the hyperbola 4 x^2 - y^2=36 at point P and Q.If these tangents intersect at point T(0,3) find area of triangle formed 

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Grade:12

1 Answers

Arun
25750 Points
5 years ago
Dear student
 
Hyperbola: 4x²-y²=36 or x²/9 -y²/36 = 1. It’s tangent may be written as: ax/9 -by/36 = 1 and it is given that it passes through (0,3). Then, 0 - 3b/36=1 or b=- 12. Substitute this in our hyperbola eqn to obtain the value of a:4a² -144=36 which yields: a = ±3√5. So P:( -3√5,-12) and Q:(3√5, -12). This implies that the height of the triangle PQT = (12+3)=15 while PQ =6√5. Area of Tr. PQT = 15*6√5/2 = 45√5 s.u.

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