The equation of the parabola whose directrix is $y = 2x - 9$ and focus is $(-8, -2)$ is:

For the parabola $y^2+6y-2x+5=0$:
$(I)$ The vertex is $(-2,-3)$
$(II)$ The directrix is $y+3=0$
Which of the following is correct?

Let a conic $C$ pass through the point $(4,-2)$ and $P(x, y), x \geq 3$,be any point on $C$. Let the slope of the line touching the conic $C$ only at a single point $P$ be half the slope of the line joining the points $P$ and $(3,-5)$. If the focal distance of the point $(7,1)$ on $C$ is $d$,then $12d$ equals ...........

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?

The line among the following which touches the parabola $y^2=4ax$ is

Find the coordinates of the focus,axis of the parabola,the equation of the directrix,and the length of the latus rectum for $y^{2}=10x$.