Tangent and normal drawn to a parabola at `A(a t^2,2a t),t!=0` meet the x-axis at point `B` and `D` , respectively. If the rectangle `A B C D` is completed, then the locus of `C` is

A straight line is drawn through P(3,4) to meet the axis of x and y at Aa n dB , respectively. If the rectangle O A C B is completed, then find the locus of Cdot

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

The tangent drawn at the point (0, 1) on the curve y=e^(2x) meets the x-axis at the point -

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

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

T P and T Q are tangents to the parabola y^2=4a x at Pa n dQ , respectively. If the chord P Q passes through the fixed point (-a ,b), then find the locus of Tdot

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 .

If t is parameter then the locus of the point P(t,(1)/(2t)) is _

Tangents PQ and PR are drawn to the parabola y^(2) = 20(x+5) and y^(2) = 60 (x+15) , respectively such that /_RPQ = (pi)/(2) . Then the locus of point P is (a) x + 10 = 0 (b) x + 30 = 0 (c) x +40 = 0 (d) x +20 = 0

If the normal to the parabola y^2=4a x at point t_1 cuts the parabola again at point t_2 , then prove that t_2^2 geq8.