Question

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)

Answer 1

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

Answer 2

Answer:

The correct option is C.

Step-by-step explanation:

The given equation is

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

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.