A point `P` moves in such a way that the ratio of its distance from two coplanar points is always a fixed number `(!=1)` . Then, identify the locus of the point.

Explanation

To solve the problem, we need to find the locus of a point \( P \) that moves such that the ratio of its distances from two fixed points \( A \) and \( B \) is a constant \( \delta \) (where \( \delta \neq 1 \)). Let's denote the coordinates of point \( A \) as \( (0, 0) \) and the coordinates of point \( B \) as \( (a, 0) \).

### Step-by-Step Solution:

1. **Define the distances**:
The distance from point \( P(x, y) \) to point \( A(0, 0) \) is given by:
\[
AP = \sqrt{x^2 + y^2}
...