Question 1042193
Endpoints to the Latus Rectum tells you the focus.  p<0 tells you the sign of the leading coefficient factor, being negative and therefore which side of the parabola to expect the focus.  Otherwise, your given information is <i>SEEMS</i> incomplete, but keep going...


x coordinate for the focus is  -1.
y coordinate for the focus is {{{(6+(-2))/2=4/2=2}}}.
Focus Point is  (-1,2).


Expect Latus Rectum to be perpendicular to axis of symmetry.  The focus in on the symmetry axis; so this axis is {{{y=2}}}.


Basic Model for standard form equation is {{{x=a(y-2)^2+h}}} for VERTEX (h,k) and you know that {{{a<0}}}, but you do not yet know nor have a directrix known.  Knowing p and a both less than 0, this parabola will open to the left.  Vertex and directrix will be located to the right of the focus.


At best, you can use the two given points:
{{{system(k=2, h=stillUnknown)}}};
{{{x=a(y-2)^2+h}}}
and then with the two given points (endpoints to Latus Recturm):
{{{system(-1=a(6-2)^2+h,-1=a(-2-2)^2+h)}}}
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SIMPLIFY these two equations, and find the values for a and h.



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You may still want some help finding value for p, finding the diredctrix, and then making the graph.