Question

The number of circles touching the line $y–x=0$ and the $y$-axis is

• A. Zero
• B. One
• C. Two
• D. Infinite

Answer 1

The correct option is D

Infinite

Explanation for correct option

There can be infinite number of circles. It's very intuitive. Draw the graph of $y–x=0$ . It's a straight line inclined to the $x$ and $y$ axes at $x=0$ line is the $y$ axis. Now just try to draw circles, touching both the lines, you will see that you can draw infinite such lines, of varying radii. That was the intuitive approach.

Hence, the correct option is $\left(\mathrm{D}\right)$, as there can be infinite number of circles.