What is 4x^2-1/2 y^2+8x+2y-2=0 ?

The solution to 4x^2-1/2 y^2+8x+2y-2=0 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=0

4 x^{2} - \frac{1}{2} y^{2} + 8 x + 2 y - 2 = 0

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

Solution steps

4 x^{2} - \frac{1}{2} y^{2} + 8 x + 2 y - 2 = 0

Rewrite

4 x^{2} - \frac{1}{2} y^{2} + 8 x + 2 y - 2 = 0

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

\frac{3}{2} (v - \frac{3}{2})^{2} - \frac{1}{2} (u + \frac{3}{2})^{2} = 6

2 x^{2} - 5 y^{2} = 13

\frac{( x - 2 ) ^{2}}{9} - \frac{( y + 3 ) ^{2}}{27} = 1

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

(\frac{y - 4}{16})^{2} - (\frac{x + 3}{36})^{2} = 1

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