Find the number of common tangents that can be drawn to the circles `x^2+y^2-4x-6y-3=0` and `x^2+y^2+2x+2y+1=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 distinct normals that can be drawn from (-2,1) to the parabola y^2-4x-2y-3=0

The number of common tangents to the circles x^(2) + y^(2) = 4 and x^(2)+y^(2)-6x-8y=24 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

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

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

An infinite number of tangents can be drawn from (1,2) to the circle x^2+y^2-2x-4y+lambda=0 . Then find the value of lambda

Find the angle at which the circles x^2+y^2+x+y=0 and x^2+y^2+x-y=0 intersect.

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