Question

the focus of a parabola is located at (4,0), and the directrix is located at x = -4. which equation represents the parabola? y² = -x y² = x y² = -16x y² = 16x

Explanation:

Step1: Recall the formula for a parabola

For a parabola with focus $(p, 0)$ and directrix $x=-p$, the standard - form equation is $y^{2}=4px$.

Step2: Identify the value of $p$

Given the focus is at $(4,0)$ and the directrix is $x = - 4$, then $p = 4$.

Step3: Substitute $p$ into the formula

Substitute $p = 4$ into $y^{2}=4px$, we get $y^{2}=4\times4x=16x$.

Answer:

$y^{2}=16x$ (corresponding to the last option in the multiple - choice list)