The focal distance of a point on the parabola $y^{2}=16x$ whose ordinate is twice the abscissa,is

The angle between the tangents drawn from the point $(1,4)$ to the parabola $y^2=4x$ 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:

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:

Statement $1$: $y = mx - \frac{1}{m}$ is always a tangent to the parabola $y^2 = -4x$ for all non-zero values of $m$.
Statement $2$: Every tangent to the parabola $y^2 = -4x$ will meet its axis at a point whose abscissa is non-negative.

How many parabolas can be drawn if the two endpoints of the latus rectum are given?