If $y = 2$ be the directrix and $(0, 1)$ be the vertex of the parabola $x^2 + \lambda y + \mu = 0$ then :
Step-by-Step Solution
Key Concept: Match the vertex and directrix equations from the transformed parabola form with given conditions to determine unknown parameters.
Given parabola $x^2 = -\lambda\left(y + \frac{\mu}{\lambda}\right)$, the vertex is at $\left(0, -\frac{\mu}{\lambda}\right)$ and directrix is $y + \frac{\mu}{\lambda} - \frac{\lambda}{4} = 0$. Comparing with given data: $-\frac{\mu}{\lambda} = 1$ and $\frac{\mu}{\lambda} - \frac{\lambda}{4} = -2$. From the first equation $\mu = -\lambda$, substituting into the second: $-1 - \frac{\lambda}{4} = -2$, giving $\lambda = 4$ and thus $\mu = -4$.
Correct Answer: 1,4