The locus of the point of intersection of the perpendicular tangents to the parabola $x^2 = 4ay$ is

The equation of the common tangent drawn to the curves $y^2 = 8x$ and $xy = -1$ is

The parametric equations of the parabola $y^2-4x-8y-12=0$ are

If the normal to the parabola $y^2 = 4ax$ intersects the axis of the parabola at a distance of $4a$ from the vertex,then the slopes of the normal are in which progression?

If the focal distance of a point $P(2, y_1)$ on the parabola $y^2=kx$ is $3$,then the equation of the tangent drawn at $P$ to the given parabola is

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 $\left( -\frac{1}{2m^2}, -\frac{1}{m} \right).$