Question 1183792
Locate the vertex, the focus, and the ends of the latus rectum and find the equation of the directrix, then draw the parabola whose equation is

{{{ (y-1)^2 = -8(x-2)}}}

vertex form

 {{{(y-k)^2 = 4p(x-h)}}}

=>{{{h=2}}}, {{{k=1}}}, {{{4p=-8}}}=> {{{p=-2 }}}

vertex at ({{{h}}}, {{{k}}} )= ({{{2}}}, {{{1 }}})

and focal length: {{{abs(p)=2}}}

parabola is symmetric around the x-axis and so the directrix is a line parallel to the y-axis, a distance:{{{-p}}} from the center ({{{2}}}, {{{1}}} ) x-coordinate

so,  directrix is a line
=>{{{x=4}}}

the latus rectum is the distance between the 2 points on the parabola that are on vertical line that goes through the focus. 

 the focus is at ({{{0}}},{{{ 1}}}), and vertical line that goes through the focus y-axis or {{{x=0}}}


{{{(y-1)^2 = -8(0-2)}}}

{{{(y-1)^2 = 16}}}

{{{y-1=sqrt(16)}}}

{{{y=4+1=5}}} or {{{y=-4+1=-3}}}

the ends of the latus rectum:({{{0}}},{{{5}}}), ({{{0}}},{{{-3}}})