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

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

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

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

(h, k) = (- \frac{1}{8}, \frac{1}{2}), a = \frac{1}{2 2}, b = \frac{1}{8}

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

\frac{( y - \frac{1}{2} ) ^{2}}{( \frac{1}{2 2} ) ^{2}} - \frac{( x - ( - \frac{1}{8} ) ) ^{2}}{( \frac{1}{8} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- \frac{1}{8}, \frac{1}{2}), a = \frac{1}{2 2}, b = \frac{1}{8}

\frac{x ^{2}}{64} - \frac{y ^{2}}{16} = 1

\frac{( x - 3 ) ^{2}}{4} - \frac{y ^{2}}{25} = 1

x^{2} - 4 y^{2} - 4 > 0

\frac{( y + 3 ) ^{2}}{9} - \frac{( x - 1 ) ^{2}}{25} = 1

x^{2} = y^{2} + 13

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