What is 2x^2-6y^2+14=0 ?

The solution to 2x^2-6y^2+14=0 is Hyperbola with (h,k)=(0,0),a=sqrt(7/3),b=sqrt(7)

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2x^2-6y^2+14=0

2 x^{2} - 6 y^{2} + 14 = 0

(h, k) = (0, 0), a = \frac{7}{3}, b = 7

Solution steps

2 x^{2} - 6 y^{2} + 14 = 0

Rewrite

2 x^{2} - 6 y^{2} + 14 = 0

in the form of a standard hyperbola equation

\frac{( y - 0 ) ^{2}}{( \frac{7}{3} ) ^{2}} - \frac{( x - 0 ) ^{2}}{( 7 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, 0), a = \frac{7}{3}, b = 7

(x + y) (x - y) \geq 1

16 x^{2} - 9 y^{2} + 96 x - 72 y + 144 = 0

\frac{x ^{2}}{81} - \frac{y ^{2}}{61} = 1

\frac{( x - 27 ) ^{2}}{3} - \frac{( y - 4 ) ^{2}}{5} = 1

2 x^{2} - 3 y^{2} = 47

What is 2x^2-6y^2+14=0 ?
The solution to 2x^2-6y^2+14=0 is Hyperbola with (h,k)=(0,0),a=sqrt(7/3),b=sqrt(7)