Find the length of the common chord of the circles `x^2+y^2+2x+6y=0` and `x^2+y^2-4x-2y-6=0`

The length of the common chord of the two circles x^2+y^2-4y=0 and x^2+y^2-8x-4y+11=0 is

If the length of the common chord of two circles x^2+y^2+8x+1=0 and x^2+y^2+2muy-1=0 is 2sqrt(6) , then the values of mu are (a) +-2 (b) +-3 (c) +-4 (d) none of these

If 2 x-3 y=0 is the equation of the common chord of the circles, x^2+y^2+4 x=0 and x^2+y^2+2 lambda y=0 , then the value of lambda is

Find the equations to the common tangents of the circles x^2+y^2-2x-6y+9=0 and x^2+y^2+6x-2y+1=0

Which of the following is a point on the common chord of the circle x^2+y^2+2x-3y+6=0 and x^2+y^2+x-8y-31=0? (a) (1,-2) (b) (1,4) (c)(1,2) (d) 1,-4)

Find the length of the common chord of the parabola y^2=4(x+3) and the circle x^2+y^2+4x=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 locus of the centres of the circle which cut the circles x^2+y^2+4x-6y+9=0 and x^2+y^2-5x+4y-2=0 orthogonally

Find the coordinates of the point at which the circles x^2-y^2-4x-2y+4=0 and x^2+y^2-12 x-8y+36=0 touch each other. Also, find equations of common tangents touching the circles the distinct points.

Find the locus of a point which moves so that the ratio of the lengths of the tangents to the circles x^2+y^2+4x+3=0 and x^2+y^2-6x+5=0 is 2: 3.