If P and Q are two points whose coordinates are `(a t^2,2a t)a n d(a/(t^2),(2a)/t)` respectively and S is the point (a,0). Show that `1/(S P)+1/(s Q)` is independent of t.

Explanation

To solve the problem, we need to show that \( \frac{1}{SP} + \frac{1}{SQ} \) is independent of \( t \), where \( P \) and \( Q \) are points with given coordinates and \( S \) is a point with given coordinates.

### Step-by-Step Solution:

1. **Identify the Coordinates:**
- The coordinates of point \( P \) are \( (at^2, 2at) \).
- The coordinates of point \( Q \) are \( \left(\frac{a}{t^2}, \frac{2a}{t}\right) \).
- The coordinates of point \( S \) are \( (a, 0) \).
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