Parabola Questions

If $a\ne 0$ and the line $2bx+3cy+4d=0$ passes through the points of intersection of the parabolas $y^2=4ax$ and $x^2=4ay,$ then

The equation of a tangent to the parabola $y^2=8x$ is $y=x+2$. The point on this line from which the other tangent to the parabola is perpendicular to the given tangent is:

Let $P$ be the point $(1,0)$ and $Q$ a point on the locus $y^2=8x$. The locus of midpoint of $PQ$ is:

The normal at the point $(b{t}_1^2,2b{t}_1)$ on a parabola meets the parabola again in the point $(b{t}_2^2,2b{t}_2)$, then:

A parabola has the origin as its focus and the line $x=2$ as the directrix. Then the vertex of the parabola is at:

If two tangents drawn from a point $P$ to the parabola $y^2=4x$ are at right angles, then the locus of $P$ is:

Statement 1: An equation of a common tangent to the parabola $y^2=16\sqrt{3}x$ and the ellipse $2x^2+y^2=4$ is $y=2x+2\sqrt{3}$.Statement 2: If the line $y=mx+\frac{4\sqrt{3}}{m},(m\ne 0)$ is a common tangent to the parabola $y^2=16\sqrt{3}x$ and the ellipse $2x^2+y^2=4$, then $m$ satisfies $m^4+2m^2=24$.

The area bounded between the parabolas $x^2=\frac{y}{4}$ and $x^2=9y$, and the straight line $y=2$ is:

A point on the parabola $y^2=18x$ at which the ordinate increases at twice the rate of the abscissa is