Question 161955
{{{x^2 - y^2 = 36}}} Start with the given equation



{{{(x-0)^2 - (y-0)^2 = 36}}} Replace "x" with "x-0". Replace "y" with "y-0"



{{{(x-0)^2/36 - (y-0)^2/36 = cross(36/36)}}} Divide EVERY term by 36 to make the right side equal to 1.



{{{(x-0)^2/36 - (y-0)^2/36 = 1}}} Reduce



{{{(x-0)^2/6^2 - (y-0)^2/6^2 = 1}}} Rewrite {{{36}}} as {{{6^2}}}



Since the last equation follows the form {{{(x-h)^2/a^2 - (y-k)^2/b^2 = 1}}} (which is the general equation of an hyperbola) where {{{h=0}}}, {{{a=6}}}, {{{k=0}}} and {{{b=6}}}, this means that the equation {{{x^2 - y^2 = 36}}} is an ellipse.



So you are correct.