The number of circles touching the line and the -axis is
Infinite
Explanation for correct option
There can be infinite number of circles. It's very intuitive. Draw the graph of . It's a straight line inclined to the and axes at line is the 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 , as there can be infinite number of circles.