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

Let $P$ and $Q$ be distinct points on the parabola $y^2=2x$ such that a circle with $PQ$ as diameter passes through the vertex $O$ of the parabola. If $P$ lies in the first quadrant and the area of the triangle $\Delta OPQ$ is $3\sqrt{2}$,then which of the following is (are) the coordinates of $P$?
$(A)$ $(4, 2\sqrt{2})$
$(B)$ $(9, 3\sqrt{2})$
$(C)$ $(\frac{1}{4}, \frac{1}{\sqrt{2}})$
$(D)$ $(1, \sqrt{2})$

If the normal drawn at $P(8, 16)$ to the parabola $y^2 = 32x$ meets the parabola again at $Q$,then the equation of the tangent drawn at $Q$ to the parabola is

What are the parametric equations of the parabola $y^2 = 8x$?

The vertex of the parabola $x^2 + 4x + 2y - 7 = 0$ is

The length of the normal chord of the parabola $y^2 = 4x$,which makes an angle of $\frac{\pi}{4}$ with the $x$-axis,is: