SOLUTION: What is the formula of 4x^2-3y^2-8x-8=0 using hyperbola?

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Question 880386: What is the formula of 4x^2-3y^2-8x-8=0 using hyperbola?
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
What do you mean, "what is the formula... using hyperbola"?

You have a quadratic equation in x and y in general form. It could be a hyperbola. You can convert the equation to standard form if you are not sure about its being a hyperbola. A bit of rearrangement with commutativity and inverses gives 4x%5E2-8x-3y%5E2=8, and then you can complete the square for x.

4%28x%5E2-2x%29-3y%5E2=8, and this seems to be a hyperbola, based on subtraction of y^2 term but addition of x^2 term.
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4%28x%5E2-2x%2B1%29-3y%5E2=8%2B4
4%28x-1%29%5E2-3y%5E2=12
highlight%28%28x-1%29%5E2%2F3-3y%5E2%2F4=1%29, hyperbola in standard form.