A rectangle PQRS has its side PQ parallel to the line `y= mx` and vertices `P, Q`, and `S` on the lines `y= a, x=b`,and `x= - b`, respectively. Find the locus of the vertex ` R`.

Explanation

To find the locus of the vertex \( R \) of the rectangle \( PQRS \) with the given conditions, we can follow these steps:

### Step 1: Define the coordinates of the vertices
Let the coordinates of the vertices be defined as follows:
- \( P(x_1, a) \) where \( y = a \)
- \( Q(b, y_1) \) where \( x = b \)
- \( S(-b, y_2) \) where \( x = -b \)
- \( R(h, k) \) where we need to find the locus.
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