A tangent is drawn at any point `P (t)` on the parabola `y^2 = 8x` and on it is taken a point `Q (alpha, beta)` from which pair of tangent QA and QB are drawn to the circle `x^2+ y^2= 4`. The locus of the point of concurrency of the chord of contact AB of the circle `x^2+y^2=4` is

A tangent is drawn at any point P(t) on the parabola y^(2)=8x and on it is takes a point Q(alpha,beta) from which a pair of tangent QA and QB are drawn to the circle x^(2)+y^(2)=8 . Using this information, answer the following questions : The point from which perpendicular tangents can be drawn both the given circle and the parabola is

Pair of tangents are drawn from origin to the circle x^2 + y^2 – 8x – 4y + 16 = 0 then square of length of chord of contact is

From points on the circle x^2+y^2=a^2 tangents are drawn to the hyperbola x^2-y^2=a^2 . Then, the locus of mid-points of the chord of contact of tangents is:

Tangents PA and PB are drawn to the circle x^(2)+y^(2)=8 from any arbitrary point P on the line x+y=4. The locus of mid-point of chord of contact AB is

From the point (4, 6) a pair of tangent lines are drawn to the parabola, y^(2) = 8x . The area of the triangle formed by these pair of tangent lines & the chord of contact of the point (4, 6) is