Question

What is the directrix of the parabola defined by `(1)/(4)(y + 3) = (x − 2)^2`? A. `y = -(49)/(16)` B. `x = -(49)/(16)` C. `y = (47)/(16)` D. `x = (47)/(16)`

Answer 1

The correct answer is y=−1/16

Answer 2

Answer:

A. $y=-\frac{49}{16}$

Step-by-step explanation:

Since, the directrix of a parabola $(x - h)^2 = 4p (y - k)$ is,

y = k - p

Here, the given parabola,

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

By comparing,

We get,

k = - 3,

$4p=\frac{1}{4}\implies p=\frac{1}{16}$

Hence, the directrix of the given parabola is,

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

$y=\frac{-48-1}{16}$

$\implies y = -\frac{49}{16}$

Option 'A' is correct.