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

If two perpendicular tangents are drawn from a point $P$ to the parabola $y^2 = 4x$,find the locus of $P$.

If the axis of a parabola is horizontal and it passes through the points $(0, 0), (0, -1)$ and $(6, 1)$,then its equation is

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

If the parabola $x^{2}=ay$ makes an intercept of length $\sqrt{40}$ units on the line $y-2x=1$,then $a$ is equal to

For the parabola $y^2 = x$,let $PQ$ be a chord such that one endpoint $P$ is $(4, -2)$ and the chord is perpendicular to the axis of the parabola. What is the slope of the normal at $Q$?