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

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

The locus of the point of intersection of two tangents to the parabola y^(2)=4ax which make the angles theta_(1) and theta_(2) with the axis so that cot theta_(1)+cot theta_(2) = c 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) .

Solve: cot5theta=cot2theta

The locus of the point of intersection of two tangents to the parabola y^(2)=4ax which make the angles theta_(1) and theta_(2) with the axis so that cot theta_(1)+cot theta_(2) = k is

From an external point P, tangent arc drawn to the the parabola y^(2) = 4ax and these tangents make angles theta_(1), theta_(2) with its axis, such that tan theta_(1) + tan theta_(2) is a constant b. Then show that P lies on the line y = bx.

Tangents to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 make angle theta_(1), theta_(2) with transvrse axis of a hyperbola. Show that the points of intersection of these tangents lies on the curve 2xy=k(x^(2)-a^(2)) when tan theta_(1)+ tan theta_(2)=k

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 :

Solve 2 tan theta-cot theta=-1 .

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).