The vertex of the parabola $(y - 2)^2 = 16(x - 1)$ is

Find the equation of the common tangent to the parabolas $y^2 = 2x$ and $x^2 = 16y$.

Let $P, Q,$ and $R$ be three co-normal points on the parabola $y^2 = 4ax$. Then the correct statement$(s)$ is/are:

From the focus of the parabola $y^2 = 12x$, a ray of light is directed in a direction making an angle $\tan^{-1} \frac{3}{4}$ with the $x$-axis. Then the equation of the line along which the reflected ray leaves the parabola 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:

If $x+5=0$ is the directrix and $(-3,0)$ is the vertex of a parabola,then the equation of this parabola is . . . . . .