If the midpoint of a chord is $(-1, 1)$,find the equation of the chord of the parabola $y^2 = 6x$.

Find the point where the normal at the point $(4, 4)$ intersects the parabola $y^2 = 4x$ again.

The locus of the points of intersection of perpendicular normals to the parabola $y^2=4ax$ is

If the parabola $y^2 = 4ax$ passes through the point $(-3, 2)$,then the length of its latus rectum is

What is the slope of the tangent drawn from the point $(4, 10)$ to the parabola $y^2 = 9x$?

Let the image of the parabola $x^{2} = 4y$ in the line $x - y = 1$ be $(y + a)^{2} = b(x - c)$, where $a, b, c \in \mathbb{N}$. Then $a + b + c$ is equal to