Answer
$y^2=2x$
Latus rectum points: $(0.5,-1),(0.5,1)$
See graph
Work Step by Step
We are given the parabola:
Vertex: $(0,0)$
Directrix: $x=-0.5$
Because the directrix is in the form $x=a$, the parabola is horizontal. Its standard equation is:
$(y-k)^2=4p(x-h)$
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 $p$:
$x=h-p=-0.5$
$0-p=-0.5$
$p=0.5$
Determine the parabola's equation:
$(y-0)^2=4(0.5)(x-0)$
$y^2=2x$
The focus is:
$(h+p,k)=(0+0.5.0)=(0.5,0)$
Determine the two points defining the latus rectum:
$x=0.5$
$y^2=2(0.5)$
$y^2=1$
$y=\pm 1$
$y=-1\Rightarrow y_1=-1$
$y=1\Rightarrow y_2=1$
$\Rightarrow (0.5,-1),(0.5,1)$
Plot the points and graph the parabola:
