What is 4x^2-1/2 y^2+8x+2y=2 ?

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

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4x^2-1/2 y^2+8x+2y=2

4 x^{2} - \frac{1}{2} y^{2} + 8 x + 2 y = 2

(h, k) = (- 1, 2), a = 1, b = 22

Solution steps

4 x^{2} - \frac{1}{2} y^{2} + 8 x + 2 y = 2

Rewrite

4 x^{2} - \frac{1}{2} y^{2} + 8 x + 2 y = 2

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (- 1, 2), a = 1, b = 22

(x - 4)^{2} - 9 (y + 7)^{2} = 1

16 x^{2} - 25 y^{2} + 96 x + 544 = 0

9 x^{2} - 4 y^{2} - 54 x + 8 y + 113 = 0

25 x^{2} + 10922 x - 25 y^{2} - y^{2} = 1439

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

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