What is 2y^2-3x^2-4y+12x+8=0 ?

The solution to 2y^2-3x^2-4y+12x+8=0 is Hyperbola with (h,k)=(2,1),a=sqrt(6),b=3

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2y^2-3x^2-4y+12x+8=0

2 y^{2} - 3 x^{2} - 4 y + 12 x + 8 = 0

(h, k) = (2, 1), a = 6, b = 3

Solution steps

2 y^{2} - 3 x^{2} - 4 y + 12 x + 8 = 0

Rewrite

2 y^{2} - 3 x^{2} - 4 y + 12 x + 8 = 0

in the form of a standard hyperbola equation

\frac{( x - 2 ) ^{2}}{( 6 ) ^{2}} - \frac{( y - 1 ) ^{2}}{3 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (2, 1), a = 6, b = 3

\frac{( x + 5 ) ^{2}}{16} - \frac{( y - 2 ) ^{2}}{36} = 1

y^{2} = x^{2} + 144

\frac{x ^{2}}{4} - \frac{3 y ^{2}}{4} = 1

y^{2} - 4 x^{2} = 12

3 x^{2} - y^{2} \leq 9

What is 2y^2-3x^2-4y+12x+8=0 ?
The solution to 2y^2-3x^2-4y+12x+8=0 is Hyperbola with (h,k)=(2,1),a=sqrt(6),b=3