Find the number of points on the $$x$$​-axis that are at a distance of 'c' units (c < 3) from the point (2, 3).

Correct option is A

Given:

We need to find the number of points on the x-axis that are at a distance c units from the point (2, 3), where c < 3.

Formula Used:

Two points A$$(x_1, y_1)$$​ and B$$(x_2, y_2)$$​​

Distance $$= \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$​

Solution:

Any point on the x-axis is of the form (x, 0).

Distance =$$\sqrt{(x - 2)^2 + (0 - 3)^2} = c$$​

​$$\sqrt{(x - 2)^2 + 9} = c$$​​

Square both sides:

​$$(x - 2)^2 + 9 = c^2$$​

​$$(x - 2)^2 = c^2 - 9$$​

Now, since c < 3,

​$$c^2 - 9 < 0$$​

​$$(x - 2)^2 < 0$$​

But the square of any real number is ≥ 0, so this inequality has no real solution.

Answer: 0