The equation of a circle is `x^2+y^2=4.` Find the center of the smallest circle touching the circle and the line `x+y=5sqrt(2)`

The centre of the smallest circle touching the circles x^2+ y^2-2y -3=0 and x^2 +y^ 2-8x -18y +93= 0 is:

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

Find the center of the smallest circle which cuts circles x^2+y^2=1 and x^2+y^2+8x+8y-33=0 orthogonally.

The equation of four circles are (x+-a)^2+(y+-a)^2=a^2 . The radius of a circle touching all the four circles is (a) (sqrt(2)+2)a (b) 2sqrt(2)a (c) (sqrt(2)+1)a (d) (2+sqrt(2))a

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

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

Find the equation of the normal to the circle x^2+y^2-2x=0 parallel to the line x+2y=3.

Find the middle point of the chord of the circle x^2+y^2=25 intercepted on the line x-2y=2

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