Question

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

Answer 1

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.

$x^{2}=\frac{1}{2}y\\ (x-0)^{2}=\frac{1}{2}(y-0)$ Where $4p=\frac{1}{2}$

From this we can easily see that $h=0\\k=0\\4p=\frac{1}{2},  p= \frac{1}{8}$.

So from the formulas given above, we can see:

Focus is $(h,k+p)=(0,0+\frac{1}{8})=(0, \frac{1}{8})$  and

Directrix is $y=k-p=0-\frac{1}{8}=- \frac{1}{8}$. So $y=-\frac{1}{8}$

ANSWER: Focus is $(0,\frac{1}{8})$ and Directrix is $y=-\frac{1}{8}$

Answer 2

Answer:

1. B.

2. A.

3. D.

4. A.

5. C.

Step-by-step explanation:

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