Question

The parabola opens to the right. The focus is given as

Answer 1

Answer:

Step-by-step explanation:

We have that the focus is at (p,0) and that the directrix is x=-p. Take the point (-p,0) of the directrix. We know that the vertex of the parabola is at the middle point ot the line segment that joins the points (p,0) and (-p,0). To get the middle piont, we take the average coordinate by coordinate. That is, the middle point is $(\frac{-p+p}{2}, \frac{0+0}{2}) = (0,0)$. The general formula of a parabola of vertex (h,k) that opens to the right or to the left is given by

$(y-k)^2 = 4p(x-h)$

Where |p| is the distance from the focus to the vertex. If the parabola opens to the right, then p>0 and p<0 otherwise. In our case, h =0=k, so we get that

$y^2 = 4px$