Question

What is the directrix of the parabola defined by 1/4(y 3)=(x-2)^2?

Answer 1

Answer:

$y = - 3.0625$

Step-by-step explanation:

The given parabola has equation:

$\frac{1}{4} (y + 3) = {(x - 2)}^{2}$

Or

${(x - 2)}^{2} = \frac{1}{4} (y + 3)$

We compare this to

${(x - h)}^{2} = 4p(y - k)$

$\implies \: 4p = \frac{1}{4}$

$p = \frac{1}{4} \div 4$

$p = \frac{1}{4} \times \frac{1}{4}$

$p = \frac{1}{16}$

The vertex of this parabola is (2,-3)

The directrix is p units below the y-value of the vertex

$y = - 3 - \frac{1}{16} = - 3.0625$