Tangents are drawn from any point on `x^2-y^2=a^2-b^2` to the ellipse `x^2/a^2+y^2/b^2=1`. If the tangents make angles `theta_1,theta_2` with the x-axis then `theta_1+theta_2=`

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))

If the tangents drawn from a point on the hyperola x^(2)-y^(2)=a^(2)-b^(2) to the ellipse x^(2)/a^(2)-y^(2)/b^(2)=1 makes angles alpha and beta with transverse axis of the hyperbola, then

Tangents drawn from (alpha , beta ) to the hyperbola x^(2) //a^(2) -y^(2)//b^(2) =1 make angles theta _1 and theta _2 with the axis .If tan theta _1 tan theta _2=1 then alpha ^(2) -beta ^(2) =

If the tangents drawn from a point on the hyperbola x^(2)-y^(2)=a^(2)-b^(2) to ellipse (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 make angle alpha and beta with the transverse axis of the hyperbola, then

If the tangents drawn from a point on the hyperbola x^(2)-y^(2)=a^(2)-b^(2) to ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 make angle alpha and beta with the transverse axis of the hyperbola, then

From an external point P, tangent arc drawn to the the parabola y^(2) = 4ax and these tangents make angles theta_(1), theta_(2) with its axis, such that tan theta_(1) + tan theta_(2) is a constant b. Then show that P lies on the line y = bx.

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 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) .

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) .