Tangents are drawn to the hyperbola `4x^(2)-y^(2)=36` at the points `P` and `Q`. If these tangents intersect at the point `T(0,3)` and the area (in sq units) of `Delta TPQ` is `a sqrt(5)` then `a=`

Tangents are drawn to the hyperbola 4x^(2)-y^(2)=36 at the points P and Q .If these tangents intersect at the point T(0,3) then the area (in sq units) of /_PTQ is

Tangents which are parrallel to the line 2x+y+8=0 are drawn to hyperbola x^(2)-y^(2)=3 . The points of contact of these tangents is/are

Tangents are drawn to the circle x^(2)+y^(2)=16 at the points where it intersects the circle x^(2)+y^(2)-6x-8y-8=0 , then the point of intersection of these tangents is

Find the points of contact Q and R of a tangent from the point P(2,3) on the parabola y^(2)=4x

The tangent and normal to the ellipse 3x^(2) + 5y^(2) = 32 at the point P(2, 2) meet the x-axis at Q and R, respectively. Then the area (in sq. units) of the triangle PQR is:

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 :

Tangents drawn to the parabola y^(2)=8x at the points P(t_(1)) and Q(t_(2)) intersect at a point T and normals at P and Q intersect at a point R such that t_(1) and t_(2) are the roots of equation t^(2)+at+2=0;|a|>2sqrt(2) then locus of R is