**Finding the Locus of the Point P**

To find the equation of the locus of a point P that satisfies the given condition, we need to determine the relationship between the distances from P to the point (6,5) and the x-axis.

Let P be a point with coordinates (x, y). We need to find the equation such that the distance from P to (6,5) is three times the distance from P to the x-axis.

**Distance Formula**

First, let's recall the distance formula. The distance between two points (x₁, y₁) and (x₂, y₂) is given by the formula:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

**Distance from P to (6,5)**

Using the distance formula, we can find the distance from P to (6,5):

d₁ = √((6 - x)² + (5 - y)²)

**Distance from P to x-axis**

The distance from P to the x-axis is simply the y-coordinate of the point P:

d₂ = y

**Equation for the Locus**

According to the given condition, the distance from P to (6,5) is three times the distance from P to the x-axis:

d₁ = 3d₂

Substituting the expressions for d₁ and d₂, we have:

√((6 - x)² + (5 - y)²) = 3y

Squaring both sides of the equation, we get:

(6 - x)² + (5 - y)² = 9y²

Expanding and simplifying the equation, we have:

36 - 12x + x² + 25 - 10y + y² = 9y²

x² - 12x + y² - 10y + 61 = 0

Therefore, the equation of the locus of the point P for which the distance from P to (6,5) is triple the distance from P to the x-axis is:

x² - 12x + y² - 10y + 61 = 0

This equation represents a circle centered at (6, 5) with a radius of √61.