The equation of the latus rectum of the parabola $x^2 + 4x + 2y = 0$ is:

The equation of the parabola whose axis is parallel to the $X$-axis and which passes through the points $(-2, 1)$,$(1, 2)$,and $(-1, 3)$ is

If $(2,3)$ is the vertex and $(3,2)$ is the focus of a parabola,then its equation is

The focus of the parabola $x^2 = -16y$ is

The maximum area of a circle centered at the origin,which is inscribed in the parabola $y = x^2 - 100$,can be expressed as $\frac{a\pi}{b}$,where $a$ and $b$ are coprime numbers. Then the value of $a + b$ is:

If a circle with its centre at the focus of the parabola $y^2 = 2px$ is such that it touches the directrix of the parabola,then a point of intersection of the circle and the parabola is