What is 2x^2-y^2+12x+8y+6=0 ?

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

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2x^2-y^2+12x+8y+6=0

2 x^{2} - y^{2} + 12 x + 8 y + 6 = 0

(h, k) = (- 3, 4), a = 2, b = 2

Solution steps

2 x^{2} - y^{2} + 12 x + 8 y + 6 = 0

Rewrite

2 x^{2} - y^{2} + 12 x + 8 y + 6 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (- 3, 4), a = 2, b = 2

36 + y^{2} - z^{2} = 4

y^{2} - 3 x^{2} = 3

9 x^{{2}} - 4 y^{{2}} = 36

y^{2} = 4 x^{2} + (- 2)

\frac{x ^{2}}{4} - \frac{y ^{2}}{9} = 4

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