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

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

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 of 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

Normals are drawn at points A, B, and C on the parabola y^2 = 4x which intersect at P. The locus of the point P if the slope of the line joining the feet of two of them is 2, is

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, T and G is

Match the following. Normals are drawn at points P Q and R lying on the parabola y^2= 4x which intersect at (3,0)

Tangent and normal at any point P of the parabola y^(2)=4ax(a gt 0) meet the x-axis at T and N respectively. If the lengths of sub-tangent and sub-normal at this point are equal, then the area of DeltaPTN is given by

Three normals are drawn from the point (7, 14) to the parabola x^2-8x-16 y=0 . Find the coordinates of the feet of the normals.

The focal chords of the parabola y^(2)=16x which are tangent to the circle of radius r and centre (6, 0) are perpendicular, then the radius r of the circle is

A normal drawn at a point P on the parabola y^2 = 4ax meets the curve again at Q. The least distance of Q from the axis of the parabola, is