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

The vertices of the base of an isosceles triangle lie on a parabola $y^2=4x$ and the base is a part of the line $y=2x-4$. If the third vertex of the triangle lies on the $X$-axis,its coordinates are

Let the tangent and normal at any point $P(at^2, 2at)$, $(a > 0)$, on the parabola $y^2 = 4ax$ meet the axis of the parabola at $T$ and $G$ respectively. Then the radius of the circle through $P, T$ and $G$ is

Let the line $y - \sqrt{3}x + 3 = 0$ cut the parabola $2y^2 = 2x + 3$ at $A$ and $B$. If $P(\sqrt{3}, 0)$,then the value of $|PA - PB|$ is [where $PA$ denotes the distance between points $P$ and $A$].

The point on the curve $y^2=2(x-3)$ at which the normal is parallel to the line $y-2x+1=0$ is

Find the minimum distance from the point $(0, c)$ to the parabola $y = x^2$,where $0 \leq c \leq 5$.