If the tangents to the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` make angles `alphaa n dbeta` with the major axis such that `tanalpha+tanbeta=gamma,` then the locus of their point of intersection is (a)`x^2+y^2=a^2` (b) `x^2+y^2=b^2` (c)`x^2-a^2=2lambdax y` (d) `lambda(x^2-a^2)=2x y`

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

Extremities of the latera recta of the ellipses (x^2)/(a^2)+(y^2)/(b^2)=1(a > b) having a given major axis 2a lies on

Find the points on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 such that the tangent at each point makes equal angles with the axes.

Find the points on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 such that the tangent at each point makes equal angles with the axes.

If the angle between the asymptotes of hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 is 120^0 and the product of perpendiculars drawn from the foci upon its any tangent is 9, then the locus of the point of intersection of perpendicular tangents of the hyperbola can be (a) x^2+y^2=6 (b) x^2+y^2=9 (c) x^2+y^2=3 (d) x^2+y^2=18

If the tangents to the parabola y^2=4a x intersect the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 at Aa n dB , then find the locus of the point of intersection of the tangents at Aa n dBdot

Any ordinate M P of the ellipse (x^2)/(25)+(y^2)/9=1 meets the auxiliary circle at Qdot Then locus of the point of intersection of normals at Pa n dQ to the respective curves is (a) x^2+y^2=8 (b) x^2+y^2=34 (c) x^2+y^2=64 (d) x^2+y^2=15

if the line x- 2y = 12 is tangent to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 at the point (3,(-9)/(2)) then the length of the latusrectum of the ellipse is

A tangent to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 cuts the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 at Pa n dQ . Show that the locus of the midpoint of P Q is ((x^2)/(a^2)+(y^2)/(b^2))^2=(x^2)/(a^2)-(y^2)/(b^2)dot