Question

For a parabola defined by the equation x^2 = 1/2y determine the focus and directrix

Answer 1

1. B.

2. A.

3. D.

4. A.

5. C.

Explanation:

Just took it

Answer 2

For a parabola in the form of
`(x-h)^(2)=4p(y-k)^(2)`, the formula for the Focus and Directrix are as follows:

Focus is given by
`(h,k+p)`, and

Directrix is given by
`y=k-p`.

Let's rearrange the given equation in the form we want.

`x^(2)=(1)/(2)y\\ (x-0)^(2)=(1)/(2)(y-0)` Where
`4p=(1)/(2)`

From this we can easily see that
`h=0\\k=0\\4p=(1)/(2),  p= (1)/(8)`.

So from the formulas given above, we can see:

Focus is
`(h,k+p)=(0,0+(1)/(8))=(0, (1)/(8))` and

Directrix is
`y=k-p=0-(1)/(8)=- (1)/(8)`. So
`y=-(1)/(8)`

ANSWER: Focus is
`(0,(1)/(8))` and Directrix is
`y=-(1)/(8)`