Question

which is the focus of a parabola with equation $y^2 = -12x$?
$(0, -3)$ $(3, 0)$ $(-3, 0)$
$(0, 3)$

Explanation:

Step1: Recall parabola standard form

The standard form of a parabola that opens left or right is \( y^2 = 4px \), where the focus is at \( (p, 0) \).

Step2: Compare with given equation

Given equation is \( y^2 = -12x \). Compare with \( y^2 = 4px \), so \( 4p = -12 \).

Step3: Solve for \( p \)

Divide both sides by 4: \( p=\frac{-12}{4}=-3 \).

Step4: Find focus coordinates

Since the parabola is of the form \( y^2 = 4px \), the focus is at \( (p, 0) \). Substituting \( p = -3 \), the focus is \( (-3, 0) \).

Answer:

\((-3, 0)\)