SOLUTION: *How to change general form to standard form y2+x+10y+26=0

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: *How to change general form to standard form y2+x+10y+26=0      Log On


   

Question 1154831: *How to change general form to standard form y2+x+10y+26=0
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

The standard form is %28x+-+h%29%5E2+=+4p+%28y+-+k%29, where the focus is (h, k+%2B+p) and the directrix is y+=+k+-+p.
If the parabola is rotated so that its vertex is (h,k) and its axis of symmetry is parallel to the x-axis, it has an equation of %28y+-+k%29%5E2+=+4p+%28x+-+h%29, where the focus is (h+%2B+p, k) and the directrix is x+=+h+-+p.
given:
y%5E2%2Bx%2B10y%2B26=0
y%5E2%2B10y=-x-26-> the parabola is rotated so you need to write it in ......b=10%2F2=5
%28y%5E2%2B10y%2B5%5E2%29-5%5E2=-x-26
%28y%2B5%29%5E2-25=-x-26
%28y%2B5%29%5E2=-x-26%2B25
%28y%2B5%29%5E2=-x-1
highlight%28%28y%2B5%29%5E2=-%28x%2B1%29%29 -> standard form

=>h=-1 and k=-5
vertex is at (-1, -5)