Ifchord ofcontact ofthe tangents drawn from the point `(alpha,beta)`to the ellipse `x^2/a^2+y^2/b^2=1`,touches the circle `x^2+y^2=c^2`, then the locus of the point

If chord of contact of the tangent drawn from the point (a,b) to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 touches the circle x^(2)+y^(2)=k^(2), then find the locus of the point (a,b).

If the chord of contact of tangents from a point (x_1,y_1) to the circle x^2+y^2=a^2 touches the circle (x-a)^2+y^2=a^2 , then the locus of (x_1,y_1) is :

If the chord of contact of tangents from a point P (x_1,y_1) to the circle x^2+y^2=a^2 touches the circle (x-a)^2+y^2 = a^2 , then the locus of (x_1, y_1) is :

If the chord of contact of tangents from a point (x_1, y_1) to the circle x^2 + y^2 = a^2 touches the circle (x-a)^2 + y^2 = a^2 , then the locus of (x_1, y_1) is

chord of contact of the tangents drawn from a point on the circle x^(2)+y^(2)=81 to the circle x^(2)+y^(2)=b^(2) touches the circle x^(2)+y^(2)=16 , then the value of b is

If the chord of contact of tangents from a point (x_(1),y_(1)) to the circle x^(2)+y^(2)=a^(2) touches the circle (x-a)^(2)+y^(2)=a^(2), then the locus of (x_(1),y_(1)) is

If the chord of contact of the tangents drawn from a point on the circle x^(2)+y^(2)+y^(2)=a^(2) to the circle x^(2)+y^(2)=b^(2) touches the circle x^(2)+y^(2)=c^(2), then prove that a,b and c are in GP.

Tangents are drawn from the point P(3, 4) to the ellipse x^2/9+y^2/4=1 touching the ellipse at points A and B.

If the chord of contact of the tangents from the point (alpha, beta) to the circle x^(2)+y^(2)=r_(1)^(2) is a tangent to the circle (x-a)^(2)+(y-b)^(2)=r_(2)^(2) , then