Question 880386
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^2-8x-3y^2=8}}}, and then you can complete the square for x.


{{{4(x^2-2x)-3y^2=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(x^2-2x+1)-3y^2=8+4}}}
{{{4(x-1)^2-3y^2=12}}}
{{{highlight((x-1)^2/3-3y^2/4=1)}}}, hyperbola in standard form.