Question

this quiz will test your knowledge on parabola foci and directrices. click the start button to begin. value: 4 find the equation of a parabola with a focus of (0, 9) and directrix y = -9. a. y = -\frac{1}{36}x^{2} b. y = \frac{1}{9}x^{2} c. y = \frac{1}{36}x^{2} d. y = -\frac{1}{9}x^{2}

Explanation:

Step1: Recall the formula for a parabola

The standard - form equation of a parabola with a vertical axis of symmetry, focus $(0,p)$ and directrix $y=-p$ is $x^{2}=4py$.

Step2: Identify the value of $p$

Given the focus is $(0,9)$ and the directrix is $y = - 9$, we have $p = 9$.

Step3: Substitute $p$ into the formula

Substituting $p = 9$ into $x^{2}=4py$, we get $x^{2}=4\times9y$, which simplifies to $x^{2}=36y$. Then, solving for $y$, we have $y=\frac{1}{36}x^{2}$.

Answer:

C. $y=\frac{1}{36}x^{2}$