What is x^2-2y^2-2x+8y+5=0 ?

The solution to x^2-2y^2-2x+8y+5=0 is Hyperbola with (h,k)=(1,2),a=sqrt(6),b=2sqrt(3)

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x^2-2y^2-2x+8y+5=0

x^{2} - 2 y^{2} - 2 x + 8 y + 5 = 0

(h, k) = (1, 2), a = 6, b = 23

Solution steps

x^{2} - 2 y^{2} - 2 x + 8 y + 5 = 0

Rewrite

x^{2} - 2 y^{2} - 2 x + 8 y + 5 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (1, 2), a = 6, b = 23

12 x^{2} - 4 y^{2} = 96

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

x^{2} - y^{2} + 6 x = 16

\frac{( y - 6 ) ^{2}}{36} - \frac{( x + 1 ) ^{2}}{16} = 1

x^{2} - y^{2} = 2^{100}

What is x^2-2y^2-2x+8y+5=0 ?
The solution to x^2-2y^2-2x+8y+5=0 is Hyperbola with (h,k)=(1,2),a=sqrt(6),b=2sqrt(3)