Consider a hyperbola H : x^2-2y^2=4. Let the tangent at a point P(4,√6) meet the x-axis at Q and latus rectum at Rx_1,y_1,x_10. If F is a focus of H…

Question

Consider a hyperbola H : x^2-2y^2=4. Let the tangent at a point P(4,√6) meet the x-axis at Q and latus rectum at Rx_1,y_1,x_1>0. If F is a focus of H which is nearer to the point P, then the area of ΔQFR (in sq. units) is equal to

MARKS Content Team · Accepted Answer

Correct answer: (C) 7√6-2. x^24-y^22=1 e=√(1+b^2a^2)=√32 ∴ Focus F(ae,0)⇒F(√6,0) equation of tangent at P to the hyperbola is 2x-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

Consider a hyperbola $H : x^{2} - 2 y^{2} = 4$ . Let the tangent at a point $P (4, \sqrt{6})$ 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

Solution

Relevant Questions

Consider a hyperbola H : x2-2y2=4. Let the tangent at a point P(4,6) meet the x-axis at Q and latus rectum at Rx1,y1,x1>0. If F is a focus of H which is nearer to the point P, then the area of ΔQFR (in sq. units) is equal to

Solution

Relevant Questions

Consider a hyperbola $H : x^{2} - 2 y^{2} = 4$ . Let the tangent at a point $P (4, \sqrt{6})$ 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