Tangents are drawn to the parabola `y^2=4a x` at the point where the line `l x+m y+n=0` meets this parabola. Find the point of intersection of these tangents.

Explanation

To solve the problem of finding the point of intersection of the tangents drawn to the parabola \( y^2 = 4ax \) at the points where the line \( lx + my + n = 0 \) intersects the parabola, we can follow these steps:

### Step 1: Find the points of intersection of the line and the parabola
We need to substitute \( y \) from the line equation into the parabola's equation.

1. Rearranging the line equation:
\[
my = -lx - n \implies y = -\frac{l}{m}x - \frac{n}{m}
...