Which of the following points lie on the parabola $x^2 = 4ay$?

Find the coordinates of the point on the parabola $y^2 = 8x$ whose focal distance is $4$.

What is the area of the triangle formed by the tangents drawn from the point $(4, 6)$ to the parabola $y^2 = 8x$ and their chord of contact?

The equation of the common tangent of the parabolas $x^2=108y$ and $y^2=32x$ is

The focus of the parabola $y^2 - x - 2y + 2 = 0$ is

The line $y - \sqrt{3}x + 3 = 0$ cuts the parabola $y^2 = x + 2$ at the points $P$ and $Q$. If the coordinates of the point $X$ are $(\sqrt{3}, 0)$, then the value of $XP \cdot XQ$ is