Two tangents drawn on parabola `y^2 = 4 ax` are making angle `alpha_1` and `alpha_2` with x-axis and if `tan^2 alpha_1+tan^2 alpha_2=c`, 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

Two tangents drawn on parabola y^(2)=4ax are making angle alpha_ _(1)and alpha_(2), with y -axis and if alpha_(1)+alpha_(2)=2 beta 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

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,

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.

Prove that sin 4alpha = 4 tan alpha (1 - tan^(2) alpha)/((1 + tan^(2) alpha)^(2))

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

Prove that sin4 alpha=4tan alpha (1- tan^(2)alpha)/((1+tan^2 alpha)^2

If the two lines ax^(2)+2hxy+by^(2)=a make angles alpha and beta with X-axis,then : tan(alpha+beta)=