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 .

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

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

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

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

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 :

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