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What is the focus of the parabola given by `-(1)/(4)(y + 2)^2 = (x −1)`? A. (-1, 2) B. (1, -2) C. (0, -2) D. (0, 2)

2 Answers

6 votes

The correct answer is that the focus is, (0,−2)

What is the focus of the parabola given by `-(1)/(4)(y + 2)^2 = (x −1)`? A. (-1, 2) B-example-1
User Eylay
by
8.3k points
5 votes

Answer:

The correct option is C.

Explanation:

The given equation is


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

Multiply both the sides by -4.


(y+2)^2=-4(x-1) .... (1)

Where, (h,k) is vertex and (h+p,k) is focus.

The standard form of a parabola is


(y-k)^2=4p(x-h) ..... (2)

From (1) and (2), we get


k=-2,h=1,4p=-4\Rightarrow p=-1

The focus of the parabola is


(h+p,k)=(1-1,-2)=(0,-2)

The focus of the given parabola is (0,-2). Therefore the correct option is C.

User Nasta
by
7.5k points

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