Question 652575
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Hi,
 y^2-2x+6y+5=0
 2x-5 =  y^2 + 6y
 2x-5 + 9 =  y^2 + 6y + 9   ||Adding 9 to both sides to complete the Square on the right side 
2x -5 + 9 =  (y+3)^2
 2x + 4 = (y+3)^2          ||Multiplying thru by 1/2
   {{{ x = (1/2)(y+3)^2 - 2}}}  Parbola, V(-2,-3), line of symmetry y = -3
 vertex form of a Parabola opening right(a>0) or left(a<0), {{{x=a(y-k)^2 +h}}}
 where(h,k) is the vertex and  y = k  is the Line of Symmetry