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?

When an air bubble of radius $r$ rises from the bottom to the surface of a lake,its radius becomes $\frac{5r}{4}$. If the atmospheric pressure is equal to the pressure exerted by a $10 \ m$ height of water column,and the temperature remains constant while surface tension is neglected,what is the depth of the lake (in $m$)?

Which of the following is Potash Alum?

If $A$ is the areal velocity of a planet of mass $M$,its angular momentum is

$A$ circular road of radius $1000 \ m$ has a banking angle of $45^o$. The maximum safe speed of a car having a mass of $2000 \ kg$ will be,if the coefficient of friction between the tyre and the road is $0.5$, . . . . . . $m/s$.

$\int_0^{\pi / 2} \sin ^8 x \cos ^2 x \, dx$ is equal to