Two tangents drawn on parabola `y^2=4ax` are making angle`alpha_1 an d alpha_2`, with x-axis and if `alpha_1+alpha_2=2beta` then locus of the point of intersection of these tangent is

Two tangents drawn on parabola y^(2)=4ax are making angle alpha_(1) and alpha_(2) with y -axis and if tan^(2)alpha_(1)+tan^(2)alpha_(2)=c, then locus of the point of intersection of these tangent is

If the tangents to ellipse x^2/a^2 + y^2/b^2 = 1 makes angle alpha and beta with major axis such that tan alpha + tan beta = lambda then locus of their point of intersection is

A pair of tangents are drawn to the parabola y^(2)=4ax which are equally inclined to a straight line y=mx+c, whose inclination to the axis is alpha. Prove that the locus of their point of intersection is the straight line y=(x-a)tan2 alpha.

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,

Tangents to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 make angles alpha and beta with the transverse axis. Find the locus of the their point of intersection if tan alpha + tan beta = k

Show that the focal chord, of parabola y^2 = 4ax , that makes an angle alpha with the x-axis is of length 4a cosec^2 alpha .

Show that the focal chord, of parabola y^2 = 4ax , that makes an angle alpha with the x-axis is of length 4a cosec^2 alpha .

Tangents are drawn to the ellipse x^2/a^2+y^2/b^2=1 at two points whose eccentric angles are alpha-beta and alpha+beta The coordinates of their point of intersection are

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