The equation of the parabola whose vertex and focus are $(0, 4)$ and $(0, 2)$ respectively,is

The equation of the tangent at $(-4, -4)$ on the curve $x^2 = -4y$ is

Which one of the following equations,represented parametrically,represents a parabolic profile?

If the tangent at a point $P,$ with parameter $t,$ on the curve $x = 4t^2 + 3, y = 8t^3 - 1, t \in R,$ meets the curve again at a point $Q,$ then the coordinates of $Q$ are

If one of the vertices of an equilateral triangle inscribed in the parabola $y^2=12x$ coincides with the vertex of the parabola, then the area (in sq. units) of that triangle is (in $\sqrt{3}$)

Statement $-1:$ The line $x - 2y = 2$ meets the parabola $y^2 + 2x = 0$ only at the point $(-2, -2).$
Statement $-2:$ The line $y = mx - \frac{1}{2m}$ $(m \neq 0)$ is tangent to the parabola $y^2 = -2x$ at the point $\left( -\frac{1}{2m^2}, -\frac{1}{m} \right).$