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 ^{2}}{16 + ( y - 4 ) ^{2}} = 1

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

16 x^{2} - 9 y^{2} - 64 x + 54 y - 161 = 0

3 x^{2} - 2 y^{2} + 6 x - 8 y - 17 = 0

x^{2} = y^{2} + 1

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