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

Tangents from point P are drawn one of each of th circle 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 o P is

Tangents from point P are drawn one of each of th circle 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 o P is

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

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

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

The number of common tangents to circles x^2+y^2+2x+8y-23=0 and x^2+y^2-4x-10y+19=0 is

Find the number of common tangent to the circles x^2+y^2+2x+8y-23=0 and x^2+y^2-4x-10 y+9=0

Find the number of common tangent to the circles x^2+y^2+2x+8y-23=0 and x^2+y^2-4x-10 y+9=0

Find the number of common tangent to the circles x^2+y^2+2x+8y-23=0 and x^2+y^2-4x-10 y+9=0

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 P is