The line $y=mx+1$ is a tangent to the curve $y^{2}=4x$ if the value of $m$ is

$A$ ray of light travelling along the line $x = 2$ strikes a parabolic mirror with the equation $y^2 - 2y - 4x + 5 = 0$ and gets reflected from its surface. Then,the equation of the reflected ray may be:

The axis of a parabola is along the line $y=x$. The distance of its vertex $A$ from $(0,0)$ is $\sqrt{2}$ and that of its focus $S$ from $(0,0)$ is $2\sqrt{2}$. If $A$ and $S$ lie in the first quadrant,then the equation of the parabola in parametric form is

What is the area of the triangle formed by the vertex of the parabola $x^2 = 12y$ and the endpoints of its latus rectum (in square units)?

Let $(x, y)$ be any point on the parabola $y^2 = 4x$. Let $P$ be the point that divides the line segment from $(0, 0)$ to $(x, y)$ in the ratio $1:3$. Then the locus of $P$ is

The length of the normal chord to the parabola $y^2 = 4x$,which subtends a right angle at the vertex,is