Find the equation of the normal to the parabola $y^2 = 4x$ which is parallel to the line $y = 3x + 4$.

If a normal is drawn to the parabola $y^2 = 4ax$ at the point $(2a, 2\sqrt{2}a)$,what is the length of the normal chord?

The point at which the line $y = mx + c$ touches the parabola $y^2 = 4ax$ is

The equations of two sides of a variable triangle are $x = 0$ and $y = 3$,and its third side is a tangent to the parabola $y^2 = 6x$. The locus of its circumcentre is:

The condition for the line $y=mx+c$ to be a normal to the parabola $y^{2}=4ax$ is

The equation of the tangent to the parabola $y^2=16x$,which is perpendicular to the line $3x-4y+5=0$,is given by