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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

\frac{( y - 2 ) ^{2}}{16} - \frac{( x + 1 ) ^{2}}{144} = 1

16 x^{2} - 160 x - 16 y^{2} - 128 y - 112 = 0

[f (x)]^{2} = 3 x^{2} - x + 2

\frac{x ^{2}}{5} - \frac{y ^{2}}{4} = 1

y^{2} = 4 + z^{2} - 2 z

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