The line $lx + my + n = 0$ will touch the parabola $y^2 = 4ax$,if

The equation of the normal to the parabola $x^2 = 8y$ at $x = 4$ is

The length of the latus rectum of the parabola $(x-2)^2+(y-3)^2=\frac{1}{25}(3x-4y+7)^2$ is

The equation of the axis of the parabola $x^2 - 4x - 3y + 10 = 0$ is:

$A$ parabola has the origin $(0,0)$ as its focus and the line $x = 2$ as the directrix. Then the vertex of the parabola is at

For the parabola $y^2 = 8x$,let $\Delta_1$ be the area of the triangle formed by the endpoints of the latus rectum and the point $P \left( \frac{1}{2}, 2 \right)$ on the parabola. Let $\Delta_2$ be the area of the triangle formed by the tangents at the endpoints of the latus rectum and the tangent at point $P$. Find the value of $\frac{\Delta_1}{\Delta_2}$.