Question

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 )

Answer 1

The equation is
`-0.25x^2-x+2=0`
The coordinates are
`((-b)/(2a);(-\Delta)/(4a))`

`\Delta=b^2-4ac=1+2=3`
The coordinates, thus, are
`((1)/(-0.5);(-1)/(-1))=(-2;1)`

Answer 2

Option B is right.

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