The equation of the normal drawn to the parabola $y^2=6x$ at the point $(24,12)$ is

What are the equations of the tangents at the endpoints of the latus rectum of the parabola $y^2 = 4ax$?

The line $y=x+1$ is a tangent to the curve $y^{2}=4x$ at the point

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 $\frac{\Delta_1}{\Delta_2}$.

The tangents to the parabola $y^2 = 4ax$ make angles $\theta_1$ and $\theta_2$ with the positive $x$-axis. If $\cot \theta_1 + \cot \theta_2 = c$,then the locus of their point of intersection is

The directrix of the parabola ${x^2 - 4x - 8y + 12 = 0}$ is