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

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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(13823) About Me  (Show Source):
You can put this solution on YOUR website!
In general, you can spot sonic sections by their equations, of the form,
Circle: %28x%29%5E2%2B%28y%29%5E2=R%5E2
Ellipse: %28x%2Fa%29%5E2%2B%28y%2Fb%29%5E2=1
Parabola: y=ax%5E2%2Bbx%2Bc
Hyperbola: %28x%2Fa%29%5E2-%28y%2Fb%29%5E2=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%5E2-y%5E2=9
%28x%2F3%29%5E2-%28y%2F3%29%5E2=1 is a hyperbola.
+graph%28+300%2C+300%2C+-5%2C+5%2C+-5%2C+5%2C+sqrt%28x%5E2-9%29%2C-sqrt%28x%5E2-9%29%29+
Your second example,
x%2By=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%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+5-x%29+