Line segment joining `(5, 0)` and `(10 costheta,10 sintheta)` is divided by a point P in ratio `2 : 3` If `theta` varies then locus of P is a ; A) Pair of straight lines C) Straight line B) Circle D) Parabola

Explanation

To find the locus of the point \( P \) that divides the line segment joining the points \( (5, 0) \) and \( (10 \cos \theta, 10 \sin \theta) \) in the ratio \( 2:3 \), we can follow these steps:

### Step 1: Use the Section Formula
The coordinates of point \( P \) that divides the line segment in the ratio \( m:n \) can be calculated using the section formula:

\[ P\left( \frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n} \right) \]
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