Let a focal chord $12x + 5y - 27 = 0$ of the parabola $y^2 = kx$ intersect the parabola at the points $P$ and $P^{\prime}$. If $S$ is the focus of this parabola,then $9(SP + SP^{\prime}) = $

If a parabola has a horizontal axis and passes through the points $(-2, 1)$,$(1, 2)$,and $(-1, 3)$,then the $y$-coordinate of the focus of that parabola is:

Three points $O(0,0)$,$P(a, a^2)$,and $Q(-b, b^2)$ with $a > 0$ and $b > 0$ lie on the parabola $y = x^2$. Let $S_1$ be the area of the region bounded by the line $PQ$ and the parabola,and $S_2$ be the area of the triangle $OPQ$. If the minimum value of $\frac{S_1}{S_2}$ is $\frac{m}{n}$,where $\operatorname{gcd}(m, n) = 1$,then $m + n$ is equal to:

The tangent drawn at any point $P$ to the parabola ${y^2} = 4ax$ meets the directrix at the point $K$. Then the angle which $KP$ subtends at its focus is ............. $^\circ$.

If $PSQ$ is a focal chord of the parabola $y^2 = 8x$ such that $SP = 6$,then find the length of $SQ$.

From a point $(d, 0)$, three normals are drawn to the parabola $y^{2} = x$. Then: