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

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

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

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

(h, k) = (4, 1), a = 1, b = 22

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (4, 1), a = 1, b = 22

9 x^{2} + 36 x - 4 y^{2} - 16 y - 16 = 0

x^{(2)} - y^{(2)} = 10 (x - y) + 1

\frac{x ^{2}}{2 0 ^{2}} - \frac{y ^{2}}{1 5 ^{2}} = 1

7 y^{2} - 14 x^{2} = 98

(\frac{x ^{2}}{36}) - \frac{y ^{2}}{25} = 1

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