The tangent at any point `P` onthe parabola `y^2=4a x` intersects the y-axis at `Qdot` Then tangent to the circumcircle of triangle `P Q S(S` is the focus) at `Q` is

If a tangent to the parabola y^2=4a x meets the x-axis at T and intersects the tangents at vertex A at P , and rectangle T A P Q is completed, then find the locus of point Qdot

If the tangent at any point P to the parabola y^(2)=4ax meets the directrix at the point K , then the angle which KP subtends at its focus is-

If the tangent at the point P(2,4) to the parabola y^2=8x meets the parabola y^2=8x+5 at Qa n dR , then find the midpoint of chord Q Rdot

Tangents PA and PB are drawn to x^2+y^2=a^2 from the point P(x_1, y_1)dot Then find the equation of the circumcircle of triangle P A Bdot

A tangent is drawn to the parabola y^2=4a x at P such that it cuts the y-axis at Qdot A line perpendicular to this tangents is drawn through Q which cuts the axis of the parabola at R . If the rectangle P Q R S is completed, then find the locus of Sdot .

Tangent is drawn at any point (p ,q) on the parabola y^2=4a xdot Tangents are drawn from any point on this tangant to the circle x^2+y^2=a^2 , such that the chords of contact pass through a fixed point (r , s) . Then p ,q ,r and s can hold the relation (a) r^2q=4p^2s (b) r q^2=4p s^2 (c) r q^2=-4p s^2 (d) r^2q=-4p^2s

If two tangents drawn from a point P to the parabola y^2 = 4x are at right angles, then the locus of P is

If the tangents at the points Pa n dQ on the parabola y^2=4a x meet at T ,a n dS is its focus, the prove that S P ,S T ,a n dS Q are in GP.

A straight line through the vertex P of a triangle P Q R intersects the side Q R at the points S and the cicumcircle of the triangle P Q R at the point Tdot If S is not the center of the circumcircle, then 1/(P S)+1/(S T) 2/(sqrt(Q SxxS R)) 1/(P S)+1/(S T) 4/(Q R)

If a tangent to the parabola y^2 = 4ax intersects the x^2/a^2+y^2/b^2= 1 at A and B , then the locus of the point of intersection of tangents at A and B to the ellipse is