Find the equation of the family of circles touching the lines `x^2-y^2+2y-1=0.`

Differential equation of the family of circles touching the line y=2 at (0,2) is

Consider four circles (x+-1)^2+(y+-1)^2=1 . Find the equation of the smaller circle touching these four circles.

Find the equation of a circle with center (4, 3) touching the circle x^2+y^2=1

Find the equation of the circle which cuts the three circles x^2+y^2-3x-6y+14=0,x^2+y^2-x-4y+8=0, and x^2+y^2+2x-6y+9=0 orthogonally.

Find the equation of the straight lines touching both x^2+y^2=2a^2 and y^2=8a xdot

2x+y=0 is the equation of a diameter of the circle which touches the lines 4x-3y+10=0 and 4x-3y-30=0. The centre and radius of the circle are

Find the locus of the center of the circle touching the circle x^2+y^2-4y=4 internally and tangents on which from (1, 2) are making of 60^0 with each other.

Find the equation of the circle which touch the line 2x-y=1 at (1,1) and line 2x+y=4

Find the equation of the smallest circle passing through the intersection of the line x+y=1 and the circle x^2+y^2=9