Question

question 3 of 10
what is the length of the focal width?
$x = \frac{1}{4}y^{2}$

Explanation:

Step1: Rewrite the equation in standard form

The standard form of a parabola opening to the right or left is $(y - k)^2=4p(x - h)$. Given $x=\frac{1}{4}y^{2}$, we can rewrite it as $y^{2}=4x$. Comparing with the standard - form $(y - 0)^2 = 4(1)(x - 0)$, we have $p = 1$.

Step2: Recall the formula for the focal width

The formula for the focal width of a parabola of the form $(y - k)^2=4p(x - h)$ (opening to the right or left) or $(x - h)^2=4p(y - k)$ (opening up or down) is $|4p|$.
Since $p = 1$, then $|4p|=4$.

Answer:

4