Question 288666
{{{x^2 - 5x + 10y + 11 = 0}}} Start with the given equation.



{{{x^2 - 5x + 10y  = -11}}} Subtract 11 from both sides.



{{{x^2 + 10y  = -11+5x}}} Add 5x to both sides



{{{10y  = -11+5x-x^2}}} Subtract {{{x^2}}} from both sides



{{{10y  = -x^2+5x-11}}} Rearrange the terms into descending degree.



{{{y  = (-x^2+5x-11)/10}}} Divide both sides by 10 to isolate 'y'.



{{{y  = (-x^2)/10+(5x)/10-11/10}}} Break up the fraction.



{{{y  = -(1/10)x^2+(1/2)x-11/10}}} Reduce and simplify.



Now that {{{y  = -(1/10)x^2+(1/2)x-11/10}}} is in the form {{{y=ax^2+bx+c}}}, which is the general equation for a parabola, this means that {{{y  = -(1/10)x^2+(1/2)x-11/10}}} is a parabola where {{{a=-1/10}}}, {{{b=1/2}}} and {{{c=-11/10}}}



Because {{{y  = -(1/10)x^2+(1/2)x-11/10}}} is equivalent to {{{x^2 - 5x + 10y + 11 = 0}}}, {{{x^2 - 5x + 10y + 11 = 0}}} is also a parabola.



So {{{x^2 - 5x + 10y + 11 = 0}}} is a parabola.