What is x^2-4y^2-4x-8y-16=0 ?

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

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x^2-4y^2-4x-8y-16=0

x^{2} - 4 y^{2} - 4 x - 8 y - 16 = 0

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

Solution steps

x^{2} - 4 y^{2} - 4 x - 8 y - 16 = 0

Rewrite

x^{2} - 4 y^{2} - 4 x - 8 y - 16 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

- 9 x^{2} + 25 y^{2} + 50 y - 200 = 0

4 x^{2} - 9 y^{2} - 144 = 0

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

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

y^{2} - 36 x^{2} = 36

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