What is 3x^2-2y^2-12x-16y+4=0 ?

The solution to 3x^2-2y^2-12x-16y+4=0 is Hyperbola with (h,k)=(2,-4),a=2sqrt(3),b=2sqrt(2)

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3x^2-2y^2-12x-16y+4=0

3 x^{2} - 2 y^{2} - 12 x - 16 y + 4 = 0

(h, k) = (2, - 4), a = 23, b = 22

Solution steps

3 x^{2} - 2 y^{2} - 12 x - 16 y + 4 = 0

Rewrite

3 x^{2} - 2 y^{2} - 12 x - 16 y + 4 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (2, - 4), a = 23, b = 22

4 x^{2} - 5 y^{2} + 32 x + 30 y = 1

3 y^{2} - 5 x^{2} + 18 y - 40 x - 533 = 0

\frac{( y - 3 ) ^{2}}{9} - \frac{( x + 1 ) ^{2}}{27} = 1

y^{2} - 4 x^{2} - 2 y + 24 x = 51

\frac{( x - 1 ) ^{2}}{36} - \frac{( y + 2 ) ^{2}}{25} = 1

What is 3x^2-2y^2-12x-16y+4=0 ?
The solution to 3x^2-2y^2-12x-16y+4=0 is Hyperbola with (h,k)=(2,-4),a=2sqrt(3),b=2sqrt(2)