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

The solution to 16y^{(2)}-x^{(2)}+2x+64y-1=0 is Hyperbola with (h,k)=(1,-2),a=2,b=8

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

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

(h, k) = (1, - 2), a = 2, b = 8

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (1, - 2), a = 2, b = 8

(\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

- 3 (x^{2} - 2 x + 1) + (y^{2} + 4 y + 2) - 2 = - 11

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

What is 16y^{(2)}-x^{(2)}+2x+64y-1=0 ?
The solution to 16y^{(2)}-x^{(2)}+2x+64y-1=0 is Hyperbola with (h,k)=(1,-2),a=2,b=8