In which quadrant does the vertex of the parabola $y^2 + 2y + x = 0$ lie?

Let $A(1, 2)$ be a point on the parabola $y^2 = 4x$. Let $B$ and $C$ be the points of intersection of this parabola with a variable line passing through the point $P(5, -2)$. Then the $\Delta ABC$ (if it exists):

Suppose $BOAC$ is a rectangle in the $XY$-plane where $O$ is the origin and $A, B$ lie on the parabola $y=x^2$. Then,$C$ must lie on the curve

If the normal to the parabola $y^2=4x$ at $P(1,2)$ meets the parabola again at $Q$,then the coordinates of $Q$ are

The number of common tangents to the parabolas $y = x^{2}$ and $y = -x^{2} + 4x - 4$ is:

Consider the parabola $25[(x-2)^2+(y+5)^2]=(3x+4y-1)^2$. Match the characteristics of this parabola given in List-$I$ with their corresponding items in List-$II$.

List-$I$	List-$II$
$I$. Vertex	$A$. $8$
$II$. Length of latus rectum	$B$. $(\frac{29}{10}, \frac{-38}{10})$
$III$. Directrix	$C$. $3x+4y-1=0$
$IV$. One end of the latus rectum	$D$. $(\frac{-2}{5}, \frac{-16}{5})$
	$E$. $6$