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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)`

Respuesta :

austint1414

The correct answer is y=−1/16

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Answer:

A. [tex]y=-\frac{49}{16}[/tex]

Step-by-step explanation:

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

y = k - p

Here, the given parabola,

[tex]\frac{1}{4}(y+3)=(x-2)^2[/tex]

By comparing,

We get,

k = - 3,

[tex]4p=\frac{1}{4}\implies p=\frac{1}{16}[/tex]

Hence, the directrix of the given parabola is,

[tex]y=-3-\frac{1}{16}[/tex]

[tex] y=\frac{-48-1}{16}[/tex]

[tex]\implies y = -\frac{49}{16}[/tex]

Option 'A' is correct.

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