The equation of the axis of the parabola $x^2 - 4x - 3y + 10 = 0$ is:

Let one end of a focal chord of the parabola $y^{2}=16x$ be $(16, 16)$. If $P(\alpha, \beta)$ divides this focal chord internally in the ratio $5 : 2$, then the minimum value of $\alpha+\beta$ is equal to:

Find the locus of the point of contact of the tangent to the parabola $y^2 = 4x$,where the tangent makes an angle of $45^{\circ}$ with the $x$-axis.

Two perpendicular tangents to the parabola $y^2 = 4ax$ always intersect on the line:

Let $P$ and $Q$ be points on the parabola $y^{2}=4x$ such that the line segment $PQ$ subtends a right angle at the vertex. If $PQ$ intersects the axis of the parabola at $R$, then the distance of the vertex from $R$ is

Let the locus of the points from which the tangents drawn to $y = x^2$ make an angle of $45^{\circ}$ with each other be $16y^2 - 16x^2 + ky + 1 = 0$. Then $k$ is equal to: