SOLUTION: 4x^2-24x-9y^2=0. How do I solve this? How do I graph this?

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Question 173591This question is from textbook Elementary and Intermediate Aalgebra
: 4x^2-24x-9y^2=0.
How do I solve this? How do I graph this? This question is from textbook Elementary and Intermediate Aalgebra

Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
4x%5E2-24x-9y%5E2=0 lets factor the x terms and complete the square
:
4%28x%5E2-6x%2B9%29-9y%5E2-9=0
:
4%28x-3%29%5E2-9y%5E2=9now divide all terms by 9
:
%284%28x-3%29%5E2%2F9%29-y%5E2=1
:
%28x-3%29%5E2%2F%283%2F2%29%5E2-y%5E2%2F%281%29%5E2=1
:
this is an equation of an hyperbola
with center at (3,0)