What is 3x^{(2)}-6x-4y^{(2)}-9=0 ?

The solution to 3x^{(2)}-6x-4y^{(2)}-9=0 is Hyperbola with (h,k)=(1,0),a=2,b=sqrt(3)

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3x^{(2)}-6x-4y^{(2)}-9=0

3 x^{(2)} - 6 x - 4 y^{(2)} - 9 = 0

(h, k) = (1, 0), a = 2, b = 3

Solution steps

3 x^{2} - 6 x - 4 y^{2} - 9 = 0

Rewrite

3 x^{2} - 6 x - 4 y^{2} - 9 = 0

in the form of a standard hyperbola equation

\frac{( x - 1 ) ^{2}}{2 ^{2}} - \frac{( y - 0 ) ^{2}}{( 3 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (1, 0), a = 2, b = 3

x^{2} - 3 y^{2} - 6 x + 12 = 0

\frac{- y ^{2}}{4} + \frac{z ^{2}}{4} = - \frac{3}{4}

2 x^{2} - y^{2} = 17

x^{2} - 4 y^{2} = 45

a^{2} - b^{2} = 8

What is 3x^{(2)}-6x-4y^{(2)}-9=0 ?
The solution to 3x^{(2)}-6x-4y^{(2)}-9=0 is Hyperbola with (h,k)=(1,0),a=2,b=sqrt(3)