Multiple Choice I

A ray of light moving parallel to the $x$-axis gets reflected from a parabolic mirror whose equation is ${\left(y-2\right)}^2=4\left(x+1\right).$ After reflection, the ray must pass through the point:

If a circle and a parabola intersect in $4$ points then the algebraic sum of the ordinates is :

If the normals from any point to the parabola $x^2=4y$ cuts the line $y=2$ in points whose abscissae are in $AP$, then the slopes of the tangents at the three conormal points are in :

Let the line $lx+my=1$ cut the parabola $y^2=4ax$ in the points $A$ and $B$. Normals at $A$ and $B$ meet at point $C$. Normal from $C$ other than these two meet the parabola at $D$ then the co-ordinates of $D$ are :

The triangle formed by the tangent to the parabola $y=x^2$ at the point whose abscissa is $x_0;x_0\in \left[1,2\right]$, the $y$-axis and the straight line $y=x_0^2$ has the greatest area if $x_0$ equal to:

A line $L$ passing through the focus of the parabola $y^2=4(x-1)$ intersects the parabola in two distinct points. If  $\text{'}m\text{'}$ be the slope of the line $L$ then

If the tangents to the parabola $y^2=4ax$ at the points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ meet at the point $\left(x_3,y_3\right)$ then :

The latus rectum of the parabola $x=a{t}^2+bt+c,y=a\text{'}{t}^2+b\text{'}t+c\text{'}$ is: