Answer
$x^2=2y$
Latus rectum points: $(-1,0.5),(1,0.5)$
See graph
Work Step by Step
We are given the parabola:
Vertex: $(0,0)$
Directrix: $y=-0.5$
Because the directrix is in the form $y=a$, the parabola is vertical. Its standard equation is:
$(x-h)^2=4p(y-k)$
Use the coordinates of the vertex to determine $h,k$:
$(h,k)=(0,0)$
$h=0$
$k=0$
Use the equation of the directrix to determine $p$:
$y=k-p=-0.5$
$0-p=-0.5$
$p=0.5$
Determine the parabola's equation:
$(x-0)^2=4(0.5)(y-0)$
$x^2=2y$
The focus is:
$(h,k+p)=(0,0+0.5)=(0,0.5)$
Determine the two points defining the latus rectum:
$y=0.5$
$x^2=2(0.5)$
$x^2=1$
$x=\pm 1$
$x=-1\Rightarrow x_1=-1$
$x=1\Rightarrow x_2=1$
$\Rightarrow (-1,0.5),(1,0.5)$
Plot the points and graph the parabola:
