Find the equation of the locus of a point which moves such that the ratio of its distances from `(2,0)a n d(1,3)` is `5: 4.`

Explanation

To find the equation of the locus of a point \( P(x, y) \) that moves such that the ratio of its distances from the points \( A(2, 0) \) and \( B(1, 3) \) is \( 5:4 \), we can follow these steps:

### Step 1: Define the distances
Let \( PA \) be the distance from point \( P \) to point \( A(2, 0) \) and \( PB \) be the distance from point \( P \) to point \( B(1, 3) \).

Using the distance formula, we have:
\[
PA = \sqrt{(x - 2)^2 + (y - 0)^2} = \sqrt{(x - 2)^2 + y^2}
...