SOLUTION: describe how the conic was formed using the concept of locus. its a parabola y^2+x+10y+26=0

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Question 1154836: describe how the conic was formed using the
concept of locus. its a parabola y^2+x+10y+26=0
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


A parabola is the locus of points equidistant from a fixed line (the directrix) and a fixed point (the focus).

Put the equation in vertex form, %28x-h%29+=+%281%2F%284p%29%29%28y-k%29%5E2

y%5E2%2Bx%2B10y%2B26=0
x+=+-y%5E2-10y-26
x+=+-1%28y%5E2%2B10y%2B26%29
x+=+-1%28y%5E2%2B10y%2B25%29-1
x+=+-1%28y%2B5%29%5E2-1
%28x%2B1%29+=+-1%28y%2B5%29%5E2

The equation in this form tells us that the vertex is at (h,k) = (-1,-5).

It also tells us that

1%2F%284p%29+=+-1 --> p+=+-1%2F4

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.

p is also the directed distance from the vertex to the focus; since the vertex is (-1,-5), the focus is (-5/4,-5).

So this parabola is the set of points equidistant from the line x=-3/4 and the point (-5/4,-5).