If the locus of mid point of any normal chord of the parabola $y^2=4 x$ is $x-\lambda=\frac{\mu}{y^2}+\frac{y^2}{v}$, where $\lambda, \mu, v \in N$, then ( $\lambda+\mu+v$ ) equals to

The line $y-\sqrt{3} x+3=0$ cuts the parabola $y^2=x+2$ at the points $P$ and $Q$. If the co-ordinates of the point $X$ are $(\sqrt{3}, 0)$, then the value of $X P \cdot X Q$ is

$$\triangle \mathrm{OAB}$$ is an equilateral triangle inscribed in the parabola $$\mathrm{y}^2=4 \mathrm{a} x, \mathrm{a}>0$$ with O as the vertex, then the length of the side of $$\triangle \mathrm{O A B}$$ is

Let A be the point (0, 4) in the xy-plane and let B be the point (2t, 0). Let L be the midpoint of AB and let the perpendicular bisector of AB meet the y-axis M. Let N be the midpoint of LM. Then locus of N is