Question

select the correct answer from each drop - down menu. a parabola is given by the equation $y^{2}=-24x$. the equation of the directrix of the parabola is. the focus of the parabola is. options for focus: (0, - 6), (6, 0), (- 6, 0), (0, 6)

Explanation:

Step1: Identify standard parabola form

The given equation $y^2=-24x$ matches the standard form $y^2=-4px$, which opens left.

Step2: Solve for $p$

Set $4p=24$, so $p=\frac{24}{4}=6$.

Step3: Find directrix equation

For $y^2=-4px$, directrix is $x=p$, so $x=6$.

Step4: Find focus coordinates

For $y^2=-4px$, focus is $(-p,0)$, so $(-6,0)$.

Answer:

1. The equation of the directrix of the parabola is $x=6$
2. The focus of the parabola is $(-6, 0)$