The length of the latus rectum of the parabola $9x^2 + 16y^2 + 24xy - 4x + 3y = 0$ is

The parabola $y^2 = x$ is symmetric about

Find the length of the chord of the parabola $y^2 = 4x$ which passes through the vertex and makes an angle of $30^{\circ}$ with the $x$-axis. (in $\sqrt{3}$)

$A$ line passes through the point $(-1, 1)$ and makes an angle $\sin^{-1}(\frac{3}{5})$ in the positive direction of the $x$-axis. If this line meets the curve $x^2 = 4y - 9$ at points $A$ and $B$,then the length $|AB|$ is equal to

If three real normals can be drawn from a point on the $x$-axis to the parabola $y^2 = 4ax$ $(a > 0)$,what is the range of the $x$-coordinate of the point?

For the parabola $y=2+4t, x=-2+2t^2$,the ends of the latus rectum are at $t=\alpha$ and $t=\beta$. Then $\alpha \beta=$