The vertex of the parabola $y^2 + 2y + x = 0$ lies in which quadrant?

If the line $y = 2x + k$ is a tangent to the curve $x^2 = 4y$,then $k$ is equal to

If the tangent to the curve $y^2 = 4x$ at point $(1, 2)$ cuts the coordinate axes at points $A$ and $B$,then the area of $\Delta AOB$ is (where $'O'$ is the origin).

If $P$ is a point which divides the line segment joining the focus of the parabola $y^2=12x$ and a point on the parabola in the ratio $1:2$,then the locus of $P$ is:

From a point $(d, 0)$, three normals are drawn to the parabola $y^{2} = x$. Then:

The focal distance of a point $(5, 5)$ on the parabola $x^2 - 2x - 4y + 5 = 0$ is