alleryFind the equation of the parabola with vertex at the origin and focus at $(0, -3)$.
A$x^2 = 12y$
B$x^2 = -12y$
C$y^2 = -12x$
D$y^2 = 12x$
Answer & Solution
Correct answer: B. $x^2 = -12y$
Focus on the **negative $y$-axis**
⇒ the parabola opens **downward** with axis along the $y$-axis. Standard form: $x^2 = -4ay$.
$|a| = 3 \Rightarrow x^2 = -12y$.
**Trap.** Option D ($y^2 = 12x$) puts the focus on the positive $x$-axis
option C on the negative $x$-axis. Always pick the standard form from the *axis* the focus lies on (vertex at origin pins the rest).
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