If the directrix of the parabola $x^2+4 y-6 x+\lambda=0$ is $y+1=0$, then which of the following is correct?

Question

Aicharya · Accepted Answer

Parabola is $(x-3)^2=-4\left(y-\left(\frac{\lambda-9}{4}ight)ight)$ Equation of direction is $y=\frac{\lambda-9}{4}+1$ $	herefore$ As direction is $y+1=0, \frac{\lambda-9}{4}+1=-1$ $\lambda=1$ $	herefore$ Vertex is $(3,-2)$ and focus is $(3,-3)$.

If the directrix of the parabola $x^2+4 y-6 x+\lambda=0$ is $y+1=0$, then which of the following is correct?

Solution