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

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 &#62; 0 . If F is a focus of H which is nearer to the point P , then the area of &#916; Q F R (in sq. units) is equal to

Quantrex Academy · Accepted Answer

Correct answer: C. 7 6 - 2

x 2 4 - y 2 2 = 1 e = 1 + b 2 a 2 = 3 2 &#8756; Focus F ( a e , 0 ) &#8658; 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 ) &#38; latus rectum x = 6 at R 6 , 2 6 6 - 1 &#8756; Area of &#916; QFR = 1 2 6 - 1 &#183; 2 6 6 - 1 = 7 6 - 2 sq. units

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

Options

Correct answer

Step-by-step solution

More from Hyperbola

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 &#62; 0 . If F is a focus of H which is nearer to the point P , then the area of &#916; Q F R (in sq. units) is equal to

Options

Correct answer

Step-by-step solution

More from Hyperbola

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