Chapter 9 - Analytic Geometry - Section 9.2 The Parabola - 9.2 Assess Your Understanding - Page 667: 19

$y^2=16x, (4,-8),(4,8)$ See graph.

1. Given the focus at $(4,0)$, vertex at $(0,0)$, we can write the parabola equation in a standard form $4px=y^2$. With $p=4$, we get $y^2=16x$ 2. Let $x=4$, we have $y^2=16(4)$ and $y=\pm8$ and the two points that define the latus rectum are $(4,-8),(4,8)$ 3. See graph.