Tangent Are Drawn From Any Point On The Hyperbola  to The Circle x2 + y2 = 9. If The Locus Of The Mid-point Of The Chord Of Contact Is   

Find the locus of the mid-points of the chord of the parabola y² = 4ax which subtend a right angle at the vertex.

If the parabola C and D intersect at a point A on the line L₁, then equation of the tangent point L at A to the parabola D is

If a > 0, the angle subtended by the chord AB at the vertex of the parabola C is

P is a point on the circle C, the perpendicular PQ to the major axis of the ellipse E meets the ellipse at M, then  is equal to

Equation of the diameter of the ellipse E conjugate to the diameter respected by L is 

If R is the point of intersection of the line L with the line x = 1, then 

If L is the chord of contact of the hyperbola H, then the equation of the corresponding pair of tangents is

If R is the point of intersection of the tangents to H at the extremities  of the chord L, then equation of the chord contact of R with respect to the parabola P is

If the chord of contact of R with respect to the parabola Pmeets the parabola at T and T’, S is the focus of the parabola, then Area of the triangle STT’ is equal to

If l is the length of the intercept made by a common tangent to the circle x² + y² = 16 and the ellipse , on the coordinate axes, then 81l²+ 3 is equal to