`P ,Q ,` and `R` are the feet of the normals drawn to a parabola `(y-3)^2=8(x-2)` . A circle cuts the above parabola at points `P ,Q ,R ,a n dS` . Then this circle always passes through the point.

Write True or False P is any point inside the circle. The tangent to the circle always passes through the point P.

The normal to the parabola y^(2)=8x at the point (2, 4) meets the parabola again at the point-

The slope of the normal to the parabola 3y^(2)+4y+2=x at a point it is 8. find the coordinates of the points.

Find the angle at which normal at point P(a t^2,2a t) to the parabola meets the parabola again at point Qdot

The common tangents to the circle x^(2)+y^(2)=2 and the parabola y^(2)=8x touch the circle at the points P, Q and the parabola at the points R, S. Then the area of the quadrilateral PQSR is

Tangent and normal are drawn at the point P-=(16 ,16) of the parabola y^2=16 x which cut the axis of the parabola at the points A and B , respectively. If the center of the circle through P ,A and B is C , then the angle between P C and the axis of x 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

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.

If the normals at P, Q, R of the parabola y^2=4ax meet in O and S be its focus, then prove that .SP . SQ . SR = a . (SO)^2 .

The common tangents to the circle x^2 + y^2 =2 and the parabola y^2 = 8x touch the circle at P,Q andthe parabola at R,S . Then area of quadrilateral PQRS is