For the parabola `y^(2)=8x` tangent and normal are drawn at P(2.4) which meet the axis of the parabola in A and B .Then the length of the diameter of the circle through A,P,B is

Tangent and normal are drawn at P(16,16) on the parabola y^2=16x which intersect the axis of the parabola at A and B respectively. If C is the centre of the circle through the points P,A and B and angle CPB=theta then the value of tan theta is

A tangent and a normal are drawn at the point P(8, 8) on the parabola y^(2)=8x which cuts the axis of the parabola at the points A and B respectively. If the centre of the circle through P, A and B is C, then the sum f sin(anglePCB) and cot(anglePCB) is equal to

The tangent and normal at the point p(18, 12) of the parabola y^(2)=8x intersects the x-axis at the point A and B respectively. The equation of the circle through P, A and B is given by

Let P be a point on the parabola, y^(2)=12x and N be the foot of the perpendicular drawn from P on the axis of the parabola. A line is now drawn through the mid-point M of PN,parallel to its axis which meets the parabola at Q. If the y-intercept of the line NQ is (4)/(3), then

Consider a parabola y^(2)=4x with vertex at A and focus at S. PQ is a chord of the parabola which is normal at point P. If the abscissa and the ordinate of the point P are equal, then the square of the length of the diameter of the circumcircle of triangle PSQ is

Normal to the parabola y^(2)=8x at the point P(2,4) meets the parabola again at the point Q . If C is the centre of the circle described on PQ as diameter then the coordinates of the image of point C in the line y=x are

The tangent and normal at P(t), for all real positive t, to the parabola y^(2)=4ax meet the axis of the parabola in T and G respectively, then the angle at which the tangent at P to the parabola is inclined to the tangent at P to the circle passing through the points P, Tand G is