Home
Class 12
MATHS
Consider a hyperbola H : x^(2)-2y^(2) =4...

Consider a hyperbola `H : x^(2)-2y^(2) =4`. Let the tangent at a point `P(4, sqrt6)` meet the x-axis at Q and latus rectum at `R (x_(1),y_(1)), x_(1) gt 0`. If F is a focus of H which is nearer to the point P, then the area of `triangleQFR` is equal to

A

`4sqrt6-1`

B

`sqrt6-1`

C

`7/sqrt6-2`

D

`4sqrt6`

Text Solution

AI Generated Solution

Promotional Banner

Similar Questions

Explore conceptually related problems

Let the curve is x^2-2y^2=4 Tangent drawn at P(4,sqrt6) cuts the x-axis at R and latus rectum at Q(x_1,y_1)(x_1 gt 0) , F be focus nearest to P. Then arDeltaQPF

Let the tangent to the parabola S : y^(2) = 2x at the point P(2,-2) meet the x-axis at Q and normal at it meet the parabola S at the point R. Then the area (in sq. units) of the triangle PQR is equal to :

The tangent at any point P on y^(2)=4x meets x-axis at Q, then locus of mid point of PQ will be

Consider a branch of the hypebola x^2-2y^2-2sqrt2x-4sqrt2y-6=0 with vertex at the point A. Let B be one of the end points of its latus rectum. If C is the focus of the hyperbola nearest to the point A, then the area of the triangle ABC is (A) 1-sqrt(2/3) (B) sqrt(3/2) -1 (C) 1+sqrt(2/3) (D) sqrt(3/2)+1

Let the tangent to the circle x^(2) + y^(2) = 25 at the point R(3, 4) meet x-axis and y-axis at points P and Q, respectively. If r is the radius of the circle passing through the origin O and having centre at the incentre of the triangle OPQ, then r^(2) is equal to :

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 3x-4y=0 and 3x+4y=0 at Q and R respectively. If O is the origin, then the area of triangle OQR is (in square units)

Consider the parabola y^(2)=4x , let P and Q be two points (4,-4) and (9,6) on the parabola. Let R be a moving point on the arc of the parabola whose x-coordinate is between P and Q. If the maximum area of triangle PQR is K, then (4K)^(1//3) is equal to

Tangent and normal at any point P of the parabola y^(2)=4ax(a gt 0) meet the x-axis at T and N respectively. If the lengths of sub-tangent and sub-normal at this point are equal, then the area of DeltaPTN is given by