The equation of the common tangent drawn to the curves $y^2 = 8x$ and $xy = -1$ is

If the normal drawn from the point $(t_1^2, 2t_1)$ to the parabola $y^2 = 4x$ intersects the parabola again at the point $(t_2^2, 2t_2)$,then -

If the parabola $y = \alpha x^{2} - 6x + \beta$ passes through the point $(0, 2)$ and has its tangent at $x = \frac{3}{2}$ parallel to the $X$-axis,then:

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

$P$ and $Q$ are the extremities of a focal chord of the parabola $y^2=4ax$. If $P=(9,9)$ and $Q=(p, q)$,then $p-q=$

If the points of intersection of the parabolas $y^2=5x$ and $x^2=5y$ lie on the line $L$,then the area of the triangle formed by the directrix of one parabola,the latus rectum of another parabola,and the line $L$ is