Suppose a parabola $y=ax^2+bx+c$ has two $x$-intercepts,one positive and one negative,and its vertex is $(2,-2)$. Then,which of the following is true?

Suppose the parabola $(y-k)^2 = 4a(x-h)$ has vertex $A$ and passes through $O = (0,0)$ and $L = (0,2)$. Let $D$ be an end point of the latus rectum. Let the $Y$-axis intersect the axis of the parabola at $P$. Then,$\angle PDA$ is equal to

The equation of a parabola which passes through the intersection points of the straight line $x + y = 0$ and the circle $x^2 + y^2 + 4y = 0$ is:

Let $P$ be a point on the parabola $x^2 = 4y$. If the distance of $P$ from the centre of the circle $x^2 + y^2 + 6x + 8 = 0$ is minimum,then the equation of the tangent to the parabola at $P$ is:

$PQ$ is a focal chord of the parabola $y^2 = 4x$ with focus $S$. If $P = (4, 4)$,then $SQ = $

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