Tangents to the ellipse `b^2x^2+a^2y^2=a^2b^2` makes angles `theta_1` and `theta_2` with major axis such that `cot(theta_1)+cot(theta_2)=k` Then the locus of the point of intersection is

Tangents to the ellipse b^(2)x^(2)+a^(2)y^(2)=a^(2)b^(2) makes angles theta_(1) and theta_(2) with major axis such that cot theta_(1)+cot(theta_(2))=k Then the locus of the point of intersection is

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

From an external point P Tangents are drawn to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 and these tangents makes angles theta_(1),theta_(2) with the axis such that cot theta_(1)+cot theta_(2)=K .Then show that all such P lies on the curve 2xy=K(y^(2)-b^(2))

(1 - cos^(2)theta)cot^(2)theta

cosec^(2)theta=1+cot^(2)theta

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

cosec^(2)theta-cot^(2)theta-1

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

Prove that cot((theta)/(2))-tan((theta)/(2))=2cot theta

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) .