Britt27
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The coordinates of the focus of the parabola −0.25x2 = y − 2 are:
A. (0, 6) B. (0, 1) C. (0, −2) D. (0, 3 )

Verified Answer :

The equation is \(-0.25x^2-x+2=0\)
The coordinates are \((\frac{-b}{2a};\frac{-\Delta}{4a})\)
\(\Delta=b^2-4ac=1+2=3\)
The coordinates, thus, are \((\frac{1}{-0.5};\frac{-1}{-1})=(-2;1)\)

Answer:

Option B is right.

Step-by-step explanation:

given is an equation of a parabola

\(-0.25x^2 =y-2\\y=-0.25x^2 +2\)

\(-x^2 =4y-8\)

Vertex is (0,2)

It is open down.

Axis of symmetry is x=0 or y axis

Hence focus will lie on axis of symmetry ie y axis.  

THe parabola has -4a = -4

Hence a = 1

SO focus will lie inside the parabola on axis of symmetry with a distance of a units from the vertex.

i.e. focus would equal = (0,2-1) = (0,1)

Option B is right

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