What is the eccentricity of a parabola?

The equation of the axis of the parabola $x^2 - 4x - 3y + 10 = 0$ is:

Let $P : y^{2} = 4ax, a > 0$ be a parabola with focus $S$. Let the tangents to the parabola $P$ that make an angle of $\frac{\pi}{4}$ with the line $y = 3x + 5$ touch the parabola $P$ at $A$ and $B$. Then the value of $a$ for which $A, B$ and $S$ are collinear is:

The equation of the tangent at a point $P(t)$,where $t$ is any parameter,to the parabola $y^2 = 4ax$ is:

The equation of the directrix of the parabola $y^2+4y+4x+2=0$ is

Find the equation of the parabola which passes through $(6,-2)$,has its vertex at the origin and its axis along the $y$-axis.