What is -3y^2-8x+4x^2-8=0 ?

The solution to -3y^2-8x+4x^2-8=0 is Hyperbola with (h,k)=(1,0),a=sqrt(3),b=2

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-3y^2-8x+4x^2-8=0

- 3 y^{2} - 8 x + 4 x^{2} - 8 = 0

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

Solution steps

- 3 y^{2} - 8 x + 4 x^{2} - 8 = 0

Rewrite

- 3 y^{2} - 8 x + 4 x^{2} - 8 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

- \frac{y ^{2}}{49} + \frac{x ^{2}}{9} = 1

18 x^{2} = 28 + 8 y^{2}

4 x^{2} - 9 y^{2} - 48 x + 108 = 0

\frac{( x - 9 ) ^{2}}{9} - \frac{( y + 4 ) ^{2}}{25} = 1

(a - b) (a + b) = 2 (3 a - 6)

What is -3y^2-8x+4x^2-8=0 ?
The solution to -3y^2-8x+4x^2-8=0 is Hyperbola with (h,k)=(1,0),a=sqrt(3),b=2