If the three normals drawn to the parabola $y^{2} = 2x$ pass through the point $(a, 0)$ where $a \neq 0$,then $a$ must be greater than:

The equation of the lines joining the vertex of the parabola $y^2 = 6x$ to the points on it whose abscissa is $24$ is:

The number of normals that can be drawn through the point $(9,6)$ to the parabola $y^2=4x$ is

From the focus of the parabola $y^2 = 12x$, a ray of light is directed in a direction making an angle $\tan^{-1} \frac{3}{4}$ with the $x$-axis. Then the equation of the line along which the reflected ray leaves the parabola is

Let a circle tangent to the directrix of a parabola $y^2 = 2ax$ have its center coinciding with the focus of the parabola. Then the points of intersection of the parabola and the circle are

If $2x + 3y + 12 = 0$ and $x - y + 4\lambda = 0$ are conjugate with respect to the parabola $y^2 = 8x$,then $\lambda$ is equal to