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

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

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

Tangents to the ellipse x^(2)//a^(2)+y^(2)//b^(2)=1 make angles theta_(1), theta_(2) with the major axis. The equation of the locus of their point of intersection when tan(theta_(1)+theta_(2))=k is

Show that the point of intersection of the tangents to the ellipse x^2/a^2+y^2/b^2=1( a gt b) which are inclined at an angle theta_1 and theta_2 with its major axis such that cot theta_1+ cot theta_2=k^2 lies on the curve k^2(y^2-b^2)=2xy

Tangents to the hyperbola x^(2)/a^(2)-y^(2)/b^(2)=1 makes angles theta_(1), theta_(2) with the transverse axis. If theta_(1), theta_(2) are complementary then the locus of the point of intersection of tangents is

Tangents to the hyperbola x^(2) //a^(2) -y^(2)//b^(2) =1 make angle theta_1 , theta _2 with the transverse axis .if theta_1 , theta _2 are complementary then the locus of the point of intcrsection of the tangents 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))

P and Q are two points on the ellipse x^2/a^2+y^2/b^2=1 with eccentric angles theta_1 and theta_2 . Find the equation of the locus of the point of intersection of the tangents at P and Q if theta_1+theta_2=pi/2 .