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

The equation of the parabola with vertex at $(0,0)$ and length of latus rectum equal to $\frac{16}{3}$ is:

Suppose that the equation $f(x) = x^{2} + bx + c = 0$ has two distinct real roots $\alpha$ and $\beta$. The angle between the tangent to the curve $y = f(x)$ at the point $\left(\frac{\alpha + \beta}{2}, f\left(\frac{\alpha + \beta}{2}\right)\right)$ and the positive direction of the $x$-axis is (in $^{\circ}$)

The axis of a parabola is parallel to the $Y$-axis. If this parabola passes through the points $(1,0), (0,2), (-1,-1)$ and its equation is $ax^2 + bx + cy + d = 0$,then $\frac{ad}{bc} = $

Find the equation of the parabola that satisfies the following conditions: Focus $(6, 0)$,directrix $x = -6$.

If $x+5=0$ is the directrix and $(-3,0)$ is the vertex of a parabola,then the equation of this parabola is . . . . . .