Let `L_1=0a n dL_2=0` be two fixed lines. A variable line is drawn through the origin to cut the two lines at `R` and `SdotPdot` is a point on the line `A B` such that `((m+n))/(O P)=m/(O R)+n/(O S)dot` Show that the locus of `P` is a straight line passing through the point of intersection of the given lines `R , S , R` are on the same side of `O)dot`

Explanation

To solve the problem, we need to show that the locus of point \( P \) is a straight line passing through the intersection of the two fixed lines \( L_1 \) and \( L_2 \).

### Step-by-Step Solution:

1. **Identify the Fixed Lines**:
Let \( L_1 \) be the line \( y = C \) and \( L_2 \) be the line \( Ax + By = 1 \).

2. **Variable Line through the Origin**:
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