Find the vertex of the parabola $y^2 + 6x - 2y + 13 = 0$.

Find the equation of the parabola whose axis is parallel to the $y$-axis and which passes through the points $(0,4), (1,9)$ and $(4,5)$.

The equation of the tangent to the parabola $y^2 = 4ax$ at the point $(3, 2)$ is . . . .

The equation of the parabola with focus $(1, -1)$ and directrix $x+y+3=0$ is

If the area of the triangle whose one vertex is at the vertex of the parabola,${y^2} + 4(x - {a^2}) = 0$ and the other two vertices are the points of intersection of the parabola and $y$-axis,is $250 \text{ sq. units}$,then a value of $a$ is

Find the angle of intersection of the curves $y^2 = 4x$ and $x^2 = 4y$.