If the tangent from a point P to the circle `x^(2)+y^(2)=1` is perpendicular to the tangent from P to the circle `x^(2)+y^(2)=3`, then the locus of P is

Show that if the length of the tangent from a point P to the circle x^2 + y^2 = a^2 be four times the length of the tangent from it to the circle (x-a)^2 + y^2 = a^2 , then P lies on the circle 15x^2 + 15y^2 - 32ax + a^2=0 .

Show that if the length of the tangent from a point P to the circle x^2 + y^2 = a^2 be four times the length of the tangent from it to the circle (x-a)^2 + y^2 = a^2 , then P lies on the circle 15x^2 + 15y^2 - 32ax + a^2=0 .

A pair of tangents are drawn from a point P to the circle x^(2)+y^(2)=1. If the tangents make an intercept of 2 on the line x=1 then the locus of P is

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

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

Two perpendicular tangents to the circle x^(2)+y^(2)=a^(2) meet at P. Then the locus of P has the equation

A pair of tangents are drawn from a point P to the circle x^2+y^2=1 . If the tangents make an intercept of 2 on the line x=1 then the locus of P is