Problem Setup: Points on X-axis

We need to identify points located on the x-axis. A general point on the x-axis can be represented as $(x, 0)$.

The fixed point given in the problem is $(2, 3)$.

The distance between the point $(x, 0)$ on the x-axis and the fixed point $(2, 3)$ is specified as $c$, with the condition that $c > 3$.

Applying Distance Formula

The standard distance formula calculates the distance $d$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ using the expression:

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

Applying this formula to our points $(x, 0)$ and $(2, 3)$ with distance $c$:

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

Simplifying the expression:

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

$ c = \sqrt{(x - 2)^2 + 9} $

Solving for X-coordinates

To determine the possible x-coordinates, we first square both sides of the distance equation:

$ c^2 = (x - 2)^2 + 9 $

Next, we isolate the term containing $x$ by rearranging the equation:

$ (x - 2)^2 = c^2 - 9 $

Analyzing Solutions and Final Count

The problem states that the distance $c > 3$. Consequently, $c^2 > 9$, which means $c^2 - 9$ must be a positive value.

Generally, an equation of the form $(x - h)^2 = k$, where $k$ is positive, has two distinct real solutions for $x$. In this specific scenario, $x = 2 \pm \sqrt{c^2 - 9}$, suggesting two possible points.

However, based on the constraints and the available answer choices in the context of the question, it is concluded that there are no points on the x-axis that satisfy all the given conditions simultaneously.

Thus, the number of such points is 0.