SOLUTION: When solving systems of relations, how do you know which conic section you will have by looking at the equation. For example: x^2-y^2=9, x+y=5

Question 105125: When solving systems of relations, how do you know which conic section you will have by looking at the equation. For example: x^2-y^2=9, x+y=5
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
In general, you can spot sonic sections by their equations, of the form,
Circle:
Ellipse:
Parabola:
Hyperbola:
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,

is a hyperbola.

Your second example,

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.