The number of circles touching the line $y - x = 0$ and the $y$-axis is
Zero
One
Two
Infinite
(d) Infinite, as there is a family of co-axial circles.
For the two circles $x^2 + y^2 = 16$ and $x^2 + y^2 -2y = 0,$ there is/are
If the circle ${x^2} + {y^2} + 6x – 2y + k = 0$ bisects the circumference of the circle ${x^2} + {y^2} + 2x – 6y – 15 = 0,$ then $k =$
Let the latus ractum of the parabola $y ^{2}=4 x$ be the common chord to the circles $C _{1}$ and $C _{2}$ each of them having radius $2 \sqrt{5}$. Then, the distance between the centres of the circles $C _{1}$ and $C _{2}$ is
The radical axis of two circles and the line joining their centres are
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