True or False:
The circle `x^2 + y^2 - 2x = 0` touches y -axis at (0,0).

If the circle x^2+y^2 +4x+22y + c = 0 bisects the circumference of the circle x^2 + y^2-2x + 8y-d = 0 ,then (c+d) is equal to

Find the equation of the circle whose radius is 5 and which touches the circle x^2 + y^2-2x- 4y- 20 = 0 externally at the point (5, 5).

Find the parametric representation of the circle x^2 + y^2 - 2x + 4y -4=0 .

The intercept on line y = x by circle x^2 + y^2- 2x = 0 is AB. Find equation of circle with AB as a diameter.

The circle x^2 + y^2+ 4x-7y + 12 = 0 cuts an intercept on y-axis equal to

The point of tangency of the circles x^2+ y^2 - 2x-4y = 0 and x^2 + y^2-8y -4 = 0 , is

For the two circles x^2+y^2= 16 and x^2+y^2-2y=0 there is/are :

Find the equation of a circle of radius 5 which lies within the circle x^2 + y^2+14x + 10y- 26 = 0 and which touches the given circle at the point (- 1, 3).

Find the equation of the image of the circle : x^2 + y^2 + 8x-16y + 64=0 in the mirror x = 0.

If the straight line ax + by = 2 ; a, b!=0 , touches the circle x^2 +y^2-2x = 3 and is normal to the circle x^2 + y^2-4y = 6 , then the values of 'a' and 'b' are ?