Two mutually perpendicular tangents of the parabola `y^2=4a x` meet the axis at `P_1a n dP_2` . If `S` is the focus of the parabola, then `1/(S P_1)` is equal to `4/a` (b) `2/1` (c) `1/a` (d) `1/(4a)`

Two mutually perpendicular tangents of the parabola y^(2)=4ax meet the axis at P_(1)andP_(2) . If S is the focal of the parabola, Then (1)/(SP_(1))+(1)/(SP_(2)) is equal to

If y=2x-3 is tangent to the parabola y^2=4a(x-1/3), then a is equal to

The tangents to the parabola y^2=4a x at the vertex V and any point P meet at Q . If S is the focus, then prove that S P,S Q , and S V are in GP.

The tangents to the parabola y^2=4x at the points (1, 2) and (4,4) meet on which of the following lines?

Tangents and normal drawn to the parabola y^2=4a x at point P(a t^2,2a t),t!=0, meet the x-axis at point Ta n dN , respectively. If S is the focus of theparabola, then (a) S P=S T!=S N (b) S P!=S T=S N (c) S P=S T=S N (d) S P!=S T!=S N

If y=m_1x+c and y=m_2x+c are two tangents to the parabola y^2+4a(x+a)=0 , then

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 to the parabola y^2=4a x at three points P ,Q ,a n dR meet at A ,a n dS is the focus, then S PdotS qdotS R is equal to a^2S A (b) S A^3 (c) a S A^2 (d) none of these

A movable parabola touches x-axis and y-axis at (0,1) and (1,0). Then the locus of the focus of the parabola is :

Two tangents on a parabola are x-y=0 and x+y=0. S(2,3) is the focus of the parabola. The length of latus rectum of the parabola is