Question 867613
{{{x^2 -4x-2y+10=0}}}


What is the question about the equation ?
It is NOT a hyperbola.  If you want as  a hyperbola, maybe you forgot to include an exponent:


{{{x^2-4x-2y^2+10=0}}}; but to be sure of which type of conic section, either do an appropriate check-test, or convert to standard form through completion of the square.  


You should find
{{{x^2-4x+4-2y^2=-10+4}}}
{{{(x-2)^2-2y^2=-6}}}
.
{{{highlight((y^2)/3-((x-2)^2)/6=1)}}}.
This would be a hyperbola with center (2,0), vertices (2, -sqrt(3)), and (2, sqrt(3)).



Actually the parabola as originally expressed in equation:
Just as simple, maybe more simple.
Same term for completing the square in x.
{{{x^2-4x-2y=-10}}}
{{{x^2-4x+10=2y}}}
{{{x^2-4x+4+10-4=2y}}}
{{{(x-2)^2+6=2y}}}
Symmetric property and mult b.sds by (1/2),
{{{highlight(y=(1/2)(x-2)^2+6)}}}.