The equation of the normal drawn to the parabola $y^2=6x$ at the point $(24,12)$ is

If the equation of the parabola with vertex $V \left(\frac{3}{2}, 3\right)$ and the directrix $x + 2y = 0$ is $\alpha x^2 + \beta y^2 - \gamma xy - 30x - 60y + 225 = 0$,then $\alpha + \beta + \gamma$ is equal to:

If $5x - 2y + k = 0$ is a tangent to the parabola $y^2 = 6x$,then their point of contact is

If $PSQ$ is the focal chord of the parabola $y^2 = 8x$ such that $SP = 6$,then the length $SQ$ is:

Let $Z$ be the point of intersection of the axis and the directrix of the parabola $4x^2 - 12x + 4y + 5 = 0$. If $S$ is its focus,then the point which divides $SZ$ in the ratio $2:1$ is

The directrix of the parabola $2 y^2+25 x=0$ is $........$