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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?
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The correct answer is:
focus is $(3,-3)$
Parabola is $(x-3)^2=-4\left(y-\left(\frac{\lambda-9}{4}\right)\right)$ Equation of direction is $y=\frac{\lambda-9}{4}+1$ $\therefore$ As direction is $y+1=0, \frac{\lambda-9}{4}+1=-1$ $\lambda=1$
$\therefore$ Vertex is $(3,-2)$ and focus is $(3,-3)$.
$\therefore$ Vertex is $(3,-2)$ and focus is $(3,-3)$.
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