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

A.
`y=-(49)/(16)`

Explanation:

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

y = k - p

Here, the given parabola,

`(1)/(4)(y+3)=(x-2)^2`

By comparing,

We get,

k = - 3,

`4p=(1)/(4)\implies p=(1)/(16)`

Hence, the directrix of the given parabola is,

`y=-3-(1)/(16)`

`y=(-48-1)/(16)`

`\implies y = -(49)/(16)`

Option 'A' is correct.