If the parabola $y^2 = 4ax$ passes through the point $(-3, 2)$,then the length of its latus rectum is

The nearest point on the curve $x^2=2y$ to the point $(0,5)$ is . . . . . . .

If $x-2y+k=0$ is a tangent to the parabola $y^2-4x-4y+8=0$,then the value of $k$ is

$A$ point on the parabola $y^2 = 18x$ at which the ordinate increases at twice the rate of the abscissa is

Let $P(x, y)$ be the midpoint of the line joining $(1, 0)$ to a point on the curve $y^{2} = \left|\begin{array}{ll}x+1 & x+2 \\ x+3 & x+5\end{array}\right|$. Then,the locus of $P$ is symmetrical about

The area of the triangle formed by the lines joining the vertex of the parabola $x^{2}=12y$ to the ends of the latus rectum is