If two tangents to the parabola `y^2=4ax` from a point `P` make angles `theta_1 and theta_2` with the axis of the parabola, then find the locus of `P` in each of the following cases. `tan^2theta_1+tan^2theta_2=lambda` (a constant)

If two tangents to the parabola y^(2)=4ax from a point P make angles theta_(1) and theta_(2) with the axis of the parabola,then find the locus of P in each of the following cases.tan^(2)theta_(1)+tan^(2)theta_(2)=lambda( a constant )

Two tangents to the parabola y^(2)=4ax make angles theta_(1),theta_(2) with the x -axis.Then the locus of their point of intersection if cot theta_(1)+cot theta_(2)=c is

Let L_(1),L_(2)andL_(3) be the three normals to the parabola y^(2)=4ax from point P inclined at the angle theta_(1),theta_(2)andtheta_(3) with x-axis, respectively. Then find the locus of point P given that theta_(1)+theta_(2)+theta_(3)=alpha (constant).

If two normals drawn from any point to the parabola y^(2) = 4ax make angle alpha and beta with the axis such that tan alpha . tan beta = 2, then find the locus of this point,

Two tangents to the parabola y^(2)=4ax make supplementary angles with the x-axis.Then the locus of their point of intersection is

Two tangents to parabola y ^(2 ) = 4ax make angles theta and phi with the x-axis. Then find the locus of their point of intersection if sin (theta - phi) =2 cos theta cos phi.

Length of the chord of the parabola y^(2)=4ax passing through the vertex and making an angle theta (0< theta < pi ) with the axis of the parabola

The length of a focal chord of the parabola y^(2)=4ax making an angle theta with the axis of the parabola is (a>0) is:

The tangent to y^(2)=ax make angles theta_(1)andtheta_(2) with the x-axis. If costheta_(1)costheta_(2)=lamda , then the locus of their point of intersection is

Tangents drawn from point P to the circle x^(2)+y^(2)=16 make the angles theta_(1) and theta_(2) with positive x-axis. Find the locus of point P such that (tan theta_(1)-tan theta_(2))=c ( constant) .