The tangent drawn to the hyperbola x 2 16 - y 2 9 = 1 , at point P in the first quadrant whose abscissa is 5, meets the lines 3 x - 4 y = 0 and 3 x + 4 y = 0 at Q and R respectively. If O is the origin, then the area of triangle O Q R is (in square units)

Question

The tangent drawn to the hyperbola x 2 16 - y 2 9 = 1 , at point P in the first quadrant whose abscissa is 5, meets the lines 3 x - 4 y = 0 and 3 x + 4 y = 0 at Q and R respectively. If O is the origin, then the area of triangle O Q R is (in square units), 6, 12, 3, 24

MARKS App · Accepted Answer

Let point P be 5 , β since it lies on given hyperbola 25 16 - β 2 9 = 1 ⇒ β 2 = 81 16 Hence, β = 9 4 (as P lies in first quadrant) So, equation of tangent is 5 x 16 - 9 y 4 ⋅ 9 = 1 ⇒ 5 x - 4 y = 16 So, points Q and R are 8 , 6 and 2 , - 3 2 Hence, the area of triangle O Q R is 1 2 12 + 12 = 12 sq. units

Search any question & find its solution

Looking for more such questions to practice?