If the tangent to the ellipse `x^2+2y^2=1` at point `P(1/(sqrt(2)),1/2)` meets the auxiliary circle at point `Ra n dQ` , then find the points of intersection of tangents to the circle at `Qa n dRdot`

If the tangents are drawn to the circle x^(2)+y^(2)=12 at the point where it meets the circle x^(2)+y^(2)-5x+3y-2=0, then find the point of intersection of these tangents.

A variable tangent to the circle x^(2)+y^(2)=1 intersects the ellipse (x^(2))/(4)+(y^(2))/(2)=1 at point P and Q. The lous of the point of the intersection of tangents to the ellipse at P and Q is another ellipse. Then find its eccentricity.

If the tangent at theta on the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 meets the auxiliary circle at two points which subtend a right angle at the centre,then e^(2)(2-cos^(2)theta)=

If the tangent at theta on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 meets the auxiliary circle at two points which subtend a right angle at the centre then e^(2)(2-cos^(2)theta) =

Tangents are drawn to the circle x^(2)+y^(2)=16 at the points where it intersects the circle x^(2)+y^(2)-6x-8y-8=0 , then the point of intersection of these tangents is

If the straight line x-2y+1=0 intersects the circle x^(2)+y^(2)=25 at points P and Q, then find the coordinates of the point of intersection of the tangents drawn at P and Q to the circle x^(2)+y^(2)=25

if a variable tangent of the circle x^(2)+y^(2)=1 intersects the ellipse x^(2)+2y^(2)=4 at P and Q. then the locus of the points of intersection of the tangents at P and Q is

Locus of point of intersection of perpendicular tangents to the circle x^(2)+y^(2)-4x-6y-1=0 is

If a tangent to the circle x^(2)+y^(2)=1 intersects the coordinate axes at distinct points P and Q, then the locus of the mid-point of PQ is :