If $y=mx+1$ is a tangent to the parabola $y^2=4x$,then $m=$

$A$ point on the parabola whose axis is parallel to the $X$-axis and which passes through the points $(0,1), (3,0), (0,-2)$ is

The slope of the line touching both the parabolas $y^2 = 4x$ and $x^2 = -32y$ is

The locus of the feet of the perpendiculars drawn from the vertex of the parabola $y^2 = 4ax$ upon all such chords of the parabola which subtend a right angle at the vertex is

$A(-1, 3)$ is a fixed point outside the parabola $y^2 = 4ax$ $(a > 0)$ and $P$ is a point moving on the parabola. The locus of point $Q$ which divides $AP$ in the ratio $3:2$ is a conic. Then the focus of that conic is

Find the equation of the parabola which is symmetric about the $y$-axis and passes through the point $(2, -3)$.