Show that the locus of the mid-point of the segment intercepted between the axes of the variable line `xcosalpha+ysinalpha = p` then `1/(x^2)+1/(y^2)=4/(p^2),` where `p` is a constant.

Explanation

To find the locus of the midpoint of the segment intercepted between the axes of the variable line \( x \cos \alpha + y \sin \alpha = p \), we will follow these steps:

### Step 1: Find the intercepts of the line
1. **Find the y-intercept**: Set \( x = 0 \) in the equation.
\[ y \sin \alpha = p \implies y = \frac{p}{\sin \alpha} \]
So, the y-intercept is \( (0, \frac{p}{\sin \alpha}) \).
...