Show that `xcosalpha+ysinalpha=p` touches the parabola `y^2=4a x` if `pcosalpha+asin^2alpha=0` and that the point of contact is `(atan^2alpha,-2atanalpha)dot`

Explanation

To show that the line \( x \cos \alpha + y \sin \alpha = p \) touches the parabola \( y^2 = 4ax \) under the condition \( p \cos \alpha + a \sin^2 \alpha = 0 \), and to find the point of contact, we can follow these steps:

### Step 1: Write the equations
The equation of the parabola is given by:
\[ y^2 = 4ax \]
The equation of the line is:
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