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

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

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

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

(h, k) = (- 3, - 4), a = 1, b = \frac{1}{2}

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (- 3, - 4), a = 1, b = \frac{1}{2}

\frac{( x + 3 ) ^{2}}{4} - \frac{( y - 1 ) ^{2}}{5} = 1

16 y^{(2)} - x^{(2)} + 2 x + 64 y - 1 = 0

(\frac{x}{7})^{2} - (\frac{y}{9})^{2} = 1

1 = 2 z^{2} - y^{2}

\frac{( y - 7 ) ^{2}}{36} - \frac{( x - 3 ) ^{2}}{64} = 1

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