What is 8y^2-x^2-16y+8x-32=0 ?

The solution to 8y^2-x^2-16y+8x-32=0 is Hyperbola with (h,k)=(4,1),a=sqrt(3),b=2sqrt(6)

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8y^2-x^2-16y+8x-32=0

8 y^{2} - x^{2} - 16 y + 8 x - 32 = 0

(h, k) = (4, 1), a = 3, b = 26

Solution steps

8 y^{2} - x^{2} - 16 y + 8 x - 32 = 0

Rewrite

8 y^{2} - x^{2} - 16 y + 8 x - 32 = 0

in the form of a standard hyperbola equation

\frac{( y - 1 ) ^{2}}{( 3 ) ^{2}} - \frac{( x - 4 ) ^{2}}{( 2 6 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (4, 1), a = 3, b = 26

2 x^{2} - y^{2} + 4 x + 2 y - 3 = 0

5 x^{2} - 2 y^{2} = 9

- x^{2} + 2 y^{2} + 28 y + 14 = 0

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

9 y^{(2)} - x^{(2)} = 36

What is 8y^2-x^2-16y+8x-32=0 ?
The solution to 8y^2-x^2-16y+8x-32=0 is Hyperbola with (h,k)=(4,1),a=sqrt(3),b=2sqrt(6)