The focus of the parabola $y^2 - x - 2y + 2 = 0$ is

Let $P(at^{2}, 2at)$,$Q$,and $R(ar^{2}, 2ar)$ be three points on the parabola $y^{2}=4ax$. If $PQ$ is a focal chord and $PK$ is parallel to $QR$,where the coordinates of $K$ are $(2a, 0)$,then the value of $r$ is:

The equation of the parabola with $(-3, 0)$ as focus and $x + 5 = 0$ as directrix is

In the $XY$-plane,three distinct lines $l_1, l_2, l_3$ concur at a point $(\lambda, 0)$. Further,the lines $l_1, l_2, l_3$ are normals to the parabola $y^2=6x$ at the points $A=(x_1, y_1)$,$B=(x_2, y_2)$,and $C=(x_3, y_3)$ respectively. Then,we have:

If $L$ is the normal drawn to the parabola $y^2 = 8x$ at the point $t = \frac{1}{\sqrt{2}}$,then the foot of the perpendicular drawn from the focus of the parabola on to the normal $L$ is

The number of normals drawn to the parabola $y^2=4x$ from the point $(1,0)$ is