SOLUTION: Put the equation in standard form for a hyperbola. 4x2−9y2−24x−54y=81

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Put the equation in standard form for a hyperbola. 4x2−9y2−24x−54y=81      Log On


   

Question 986810: Put the equation in standard form for a hyperbola.
4x2−9y2−24x−54y=81
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
4x%5E2-24x-9y%5E2-54y=81
4%28x%5E2-6x%29-9%28y%5E2%2B6y%29=81
term to complete the square for each of the quadratic factors INSIDE the grouping symbols is %286%2F2%29%5E2=9.
4%28x%5E2-6x%2B9%29-9%28y%5E2%2B6y%2B9%29=81%2B4%2A9-9%2A9-----you need to clearly understand this step;
4%28x-3%29%5E2-9%28y%2B3%29%5E2=9%289%2B4-9%29
4%28x-3%29%5E2-9%28y%2B3%29%5E2=9%2A4
%28x-3%29%5E2%2F9-%28y%2B3%29%5E2%2F4=1


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Explanations for Completing The Square:
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Lesson on how to solve, but includes how to choose the term to Complete The Square, and how to perform the process
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Visual explanation of what Completing The Square means