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

Algebra ->  Algebra  -> Quadratic-relations-and-conic-sections -> SOLUTION: 4x^2-24x-9y^2=0. How do I solve this? How do I graph this?      Log On

Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

   

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)

drawing%28+300%2C+300%2C+-5%2C+5%2C+-5%2C+5%2C+%0D%0A+++++++++grid%281%29%2C%0D%0A+++++++++blue%28+hyperbola%28+3%2C0%2C+3%2C+1+%29+%0D%0A+++++++++%29%29