If the graph of $y = ax^2 - bx + c$ is as shown below,then the signs of $a$,$b$,and $c$ are:

The parabola with directrix $x+2y-1=0$ and focus $(1,0)$ is

If the locus of a point which divides a chord with slope $2$ of the parabola $y^2=4x$ internally in the ratio $1:3$ is a parabola,then its vertex is

The points on the parabola $y^2 = 36x$ whose ordinate is three times the abscissa are

Find the angle of intersection between the curves $y^2 = 4ax$ and $x^2 = 4ay$.

Let a conic $C$ pass through the point $(4,-2)$ and $P(x, y), x \geq 3$,be any point on $C$. Let the slope of the line touching the conic $C$ only at a single point $P$ be half the slope of the line joining the points $P$ and $(3,-5)$. If the focal distance of the point $(7,1)$ on $C$ is $d$,then $12d$ equals ...........