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

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

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

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

(h, k) = (1, - 4), a = 1, b = 2

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (1, - 4), a = 1, b = 2

9 x^{2} - 25 y^{2} - 90 x + 50 y - 25 = 0

\frac{( y + 5 ) ^{2}}{81} - \frac{( x + 8 ) ^{2}}{9} = 1

x^{2} - y^{2} - 1 = 3 x - 3 y

3 x^{2} - 3 y^{2} + 2 x + 14 y + 24 = 0

y^{2} = 4 x^{2} - 15

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