Question 1154836
<br>
A parabola is the locus of points equidistant from a fixed line (the directrix) and a fixed point (the focus).<br>
Put the equation in vertex form, {{{(x-h) = (1/(4p))(y-k)^2}}}<br>
{{{y^2+x+10y+26=0}}}
{{{x = -y^2-10y-26}}}
{{{x = -1(y^2+10y+26)}}}
{{{x = -1(y^2+10y+25)-1}}}
{{{x = -1(y+5)^2-1}}}
{{{(x+1) = -1(y+5)^2}}}<br>
The equation in this form tells us that the vertex is at (h,k) = (-1,-5).<br>
It also tells us that<br>
{{{1/(4p) = -1}}} --> {{{p = -1/4}}}<br>
p is the directed distance from the directrix to the vertex, so from the directrix to the vertex is -1/4.  Since the vertex is (-1,-5), the directrix is the line x = -3/4.<br>
p is also the directed distance from the vertex to the focus; since the vertex is (-1,-5), the focus is (-5/4,-5).<br>
So this parabola is the set of points equidistant from the line x=-3/4 and the point (-5/4,-5).<br>