The tangents to `x^2+y^2=a^2` having inclinations `alpha` and `beta` intersect at `Pdot` If `cotalpha+cotbeta=0` , then find the locus of `Pdot`

The tangents to x^(2)+y^(2)=r^(2) having inclinations theta_(1),theta_(2) intersect at P .If tan theta_(1)-tan theta_(2)=1 locus of P is

If the tangents to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 make angles alpha and beta with the major axis such that tan alpha+tan beta=gamma ,then the locus of their point of intersection is x^(2)+y^(2)=a^(2)(b)x^(2)+y^(2)=b^(2)x^(2)-a^(2)=2 lambda xy(d)lambda(x^(2)-a^(2))=2xy

If (alpha , beta) is the point on y^2=6x , that is closest to (3,3/2) then find the value of 2(alpha+beta)

Prove that the locus of a point,tangents from where to hyperbola x^(2)-y^(2)=a^(2) inclined at an angle alpha& beta with x-axis such that tan alpha tan beta=2 is also a hyperbola.Find the eccentricity of this hyperbola.

If the eccentric angles of two points P and Q on the ellipse x^2/a^2+y^2/b^2 are alpha,beta such that alpha +beta=pi/2 , then the locus of the point of intersection of the normals at P and Q is

If alpha and beta are the roots of the equation x^(2) -x+7=0 , then find the value of alpha^(2) + beta^(2) .

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

Find the condition that the chord of contact of tangents from the point (alpha, beta) to the circle x^2 + y^2 = a^2 should subtend a right angle at the centre. Hence find the locus of (alpha, beta) .

A circle x^(2)+y^(2)=a^(2) meets the x-axis at A(-a,0) and B(a,0). P(alpha) and Q( beta ) are two points on the circle so that alpha-beta=2 gamma, where gamma is a constant. Find the locus of the point of intersection of AP and BQ.

If the tangents to the parabola y^(2)=4ax intersect the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at A and B, then find the locus of the point of intersection of the tangents at A and B.