The equation of the tangent to the parabola $y^2=12x$ at the point $(3,-6)$ 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 curve described parametrically by $x = t^2 + t + 1$ and $y = t^2 - t + 1$ represents:

The equation of a straight line drawn through the focus of the parabola $y^2 = -4x$ at an angle of $120^\circ$ to the $x$-axis is:

The length of the latus rectum of the parabola $169\{(x-1)^2+(y-3)^2\}=(5x-12y+17)^2$ is

If $a > 0$ and $b^2 - 4ac = 0$,then the curve $y = ax^2 + bx + c$