The vertex of the parabola $x^2 + 8x + 12y + 4 = 0$ is

What is the length of the chord intercepted by the parabola $y = x^2 + 3x$ on the line $x + y = 5$?

The equation of the parabola with the focus $(3,0)$ and the directrix $x+3=0$ is:

If $0 \leq x \leq 5$,then the minimum distance from the point $(0, c)$ to the parabola $y = x^2$ is:

The equation of the parabola whose axis is parallel to the $X$-axis and which passes through the points $(-2, 1)$,$(1, 2)$,and $(-1, 3)$ is

If the line $2x + 3y + n = 0$ is a tangent to the parabola $y^2 = 8x$,then the equation of the normal drawn at the point $(2n, 4\sqrt{n})$ to the parabola $y^2 = 8x$ is