Consider a hyperbola H : x 2 - 2 y 2 = 4 . Let the tangent at a point P ( 4 , 6 ) meet the x -axis at Q and latus rectum at R x 1 , y 1 , x 1 0 . If F is a focus of H which is nearer to the point P

Question

Consider a hyperbola H : x 2 - 2 y 2 = 4 . Let the tangent at a point P ( 4 , 6 ) meet the x -axis at Q and latus rectum at R x 1 , y 1 , x 1 > 0 . If F is a focus of H which is nearer to the point P , then the area of Δ Q F R (in sq. units) is equal to

TestHub · Accepted Answer

x 2 4 - y 2 2 = 1 e = 1 + b 2 a 2 = 3 2 ∴ Focus F ( a e , 0 ) ⇒ F ( 6 , 0 ) equation of tangent at P to the hyperbola is 2 x - y 6 = 2 tangent meet x -axis at Q ( 1 , 0 ) & latus rectum x = 6 at R 6 , 2 6 6 - 1 ∴ Area of Δ QFR = 1 2 6 - 1 · 2 6 6 - 1 = 7 6 - 2 sq. units

Mathematics - Hyperbola Question with Solution | TestHub

Options:

Doubts & Discussion