If $2x + y + \lambda = 0$ is a focal chord of the parabola $y^2 = -8x$,find the value of $\lambda$.

If the normal drawn at the point $P(9, 9)$ on the parabola $y^2 = 9x$ meets the parabola again at $Q(a, b)$,then $2a + b =$

Let $y^{2}=12x$ be the parabola with its vertex at $O(0,0)$. Let $P$ be a point on the parabola and $A$ be a point on the $x$-axis such that $\angle OPA=90^{\circ}$. Then the locus of the centroid of such triangles $OPA$ is:

The angle subtended by the normal chord at the point $(9, 9)$ on the parabola $y^2 = 9x$ at the focus of the parabola is (in $^{\circ}$)

The point on the parabola $y^2 = 18x$,for which the ordinate is three times the abscissa,is

If tangent lines are drawn from the point $(-1, 2)$ to the parabola $y^2 = 4x$, then the area of the triangle (in sq. units) formed by the chord of contact and the tangents drawn is: (in $\sqrt{2}$)