The equation of the tangent to the parabola $y^2 = 9x$ which passes through the point $(4, 10)$ is:

Three normals to the parabola $y^2 = x$ are drawn through a point $(C, 0)$. Then:

Let the directrix of the parabola $P : y^2 = 8x$, cut $x$-axis at the point $A$. Let $B(\alpha, \beta)$, $\alpha > 1$, be a point on $P$ such that the slope of $AB$ is $3/5$. If $BC$ is a focal chord of $P$, then six times the area of $\triangle ABC$ is :

The locus of the foot of the perpendicular drawn from the focus to any tangent of the parabola $y^2 = 4ax$ is:

Let $P : y^{2} = 4ax, a > 0$ be a parabola with focus $S$. Let the tangents to the parabola $P$ that make an angle of $\frac{\pi}{4}$ with the line $y = 3x + 5$ touch the parabola $P$ at $A$ and $B$. Then the value of $a$ for which $A, B$ and $S$ are collinear is:

The equation of the chord of contact of the tangents drawn from the point $(2, 3)$ to the parabola $y^2 + x = 0$ is: