Answer:
12 units
Step-by-step explanation:
The lactus rectum for a parabola is equal to 4 times the length of the focus from the vertex. Therefore, we need to determine the focus [tex](h+p,k)[/tex] by using the equation [tex](y-k)^2=4p(x-h)[/tex] for a vertical parabola.
We can deduce that [tex]k=-3[/tex], [tex]h=1[/tex], and [tex]p=3[/tex]. Therefore, the focus of the parabola is [tex](1+3,-3)[/tex] or [tex](4,-3)[/tex].
Because the focus is [tex](4,-3)[/tex], then it is 3 units away from the vertex [tex](4,0)[/tex], making the length of the latus rectum 3*4=12 units.
