4x2-8x-9y2+54x=113
(4x2-8x ) + (-9y2+54y ) =113
4(x2-2x+1) -9(y2-6y+9) =113+4-81 because of distribution
4(x-1)2 - 9(y-3)2 = 36
Divide by 36
(x-1)2 - (y-3)2 =1
9 4
True
true
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It's an hyperbola equation.
hyperbola
y2-3x2+6x+6y= 18 is in standard form. The vertex form would be (y+3)2/24 - (x-1)2/8 = 1
You cannot solve this single equation. You can either change the subject so that it gives x = 12/y or xy = 12, which is the equation of a rectangular hyperbola.
true
2
9
x = 4.5
It depends on what you are calling "standard form". 2x = 7 can be solved, but it is a standard form of an algebraic equation.