Find the coordinates of the focus,axis of the parabola,the equation of the directrix,and the length of the latus rectum for $x^{2}=6y$.

If the tangent at a point $P$ on a parabola makes an angle $\alpha$ with its focal distance,then the angle between the tangent and the axis of the parabola is:

The shortest distance between the line $y-x=1$ and the curve $x=y^2$ is

If $P(h, k)$ is a point on the parabola $x = 4y^2$ which is nearest to the point $Q(0, 33)$,then the distance of $P$ from the directrix of the parabola $y^2 = 4(x + y)$ is equal to:

$A$ quadratic polynomial $y = f(x)$ with absolute term $3$ neither touches nor intersects the abscissa axis and is symmetric about the line $x = 1$. The coefficient of the leading term of the polynomial is unity. $A$ point $A(x_1, y_1)$ with abscissa $x_1 = 1$ and a point $B(x_2, y_2)$ with ordinate $y_2 = 11$ are given in a Cartesian rectangular system of coordinates $OXY$ in the first quadrant on the curve $y = f(x)$,where $O$ is the origin. The graph of $y = f(x)$ represents a parabola whose focus has the coordinates:

The point on the parabola $y^2 = 8x$ at which the normal is inclined at $60^\circ$ to the $x$-axis has the coordinates: