Question

Identify the vertex, focus, and directrix of the parabola who’s equation is y^2=2x

Answer 1

y² = 2x  ⇒  x = $\frac{1}{2} y^{2}$

vertex (0, 0)

focus: $\frac{1}{4p} = \frac{1}{2}$   ⇒  p = $\frac{1}{2}$ so focus is: ($\frac{1}{2}$ , 0)

directrix: x = $-\frac{1}{2}$