Question 105125
In general, you can spot sonic sections by their equations, of the form,
Circle: {{{(x)^2+(y)^2=R^2}}} 
Ellipse: {{{(x/a)^2+(y/b)^2=1}}} 
Parabola:  {{{y=ax^2+bx+c}}}
Hyperbola:  {{{(x/a)^2-(y/b)^2=1}}}
Sometimes your equation will not look so neat and you'll have to do some manipulation to get it to look like these standard forms. 
Your first example, 
{{{x^2-y^2=9}}}
{{{(x/3)^2-(y/3)^2=1}}} is a hyperbola. 
{{{ graph( 300, 300, -5, 5, -5, 5, sqrt(x^2-9),-sqrt(x^2-9)) }}}
Your second example, 
{{{x+y=5}}}
{{{y=5-x}}} is a linear equation, yielding a straight line, and is not a conic section. 
It has a slope of -1 and a y-intercept of 5. 
{{{ graph( 300, 300, -10, 10, -10, 10, 5-x) }}}