Tangents from point P are drawn one to each of the circles `x^2+y^2-4x-8y+11=0` and `x^2+y^2-4x-8y+15=0` if the tangents are perpendicular then the locus of P is

The point of tangency of the circles x^(2)+y^(2)-2x-4y=0 and x^(2)+y^(2)-8y-4=0 is

A tangent is drawn to each of the circles x^(2)+y^(2)=a^(2) and x^(2)+y^(2)=b^(2). Show that if the two tangents are mutually perpendicular, the locus of their point of intersection is a circle concentric with the given circles.

If the lengths of the tangents drawn from P to the circles x ^(2) + y ^(2) -2x + 4y -20=0 and x ^(2) + y^(2) -2x -8y +1=0 are in the ratio 2:1 , then the locus of p is

Find the angle between the circles S:x^(2)+y^(2)-4x+6y+11=0andS':x^(2)+y^(2)-2x+8y+13=0

Tangents are drawn from a point P on the line y=4 to the circle x^(2)+y^(2)=25 .If the tangents are perpendicular to each other,then coordinates of P are

If tangents are drawn from origin to the circle x^(2)+y^(2)-2x-4y+4=0, then

The point lying on common tangent to the circles x^(2)+y^(2)=4 and x^(2)+y^(2)+6x+8y-24=0 is