For the parabola $y^2 = 8x$,what is the position of the point $(2, 5)$?

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 equation of the tangent to the parabola $y^{2}=16x$ at the point $P(3, 6)$ is:

The equation of the tangent at a point $P(t)$,where $t$ is any parameter,to the parabola $y^2 = 4ax$ is:

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

The equation of the parabola whose focus is the point $(0, 0)$ and the tangent at the vertex is $x - y + 1 = 0$ is