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

The solution to x^2-4y^2+2x-1y-4=0 is Hyperbola with (h,k)=(-1,-1/8),a=(sqrt(79))/4 ,b=(sqrt(79))/8

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x^2-4y^2+2x-1y-4=0

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

(h, k) = (- 1, - \frac{1}{8}), a = \frac{79}{4}, b = \frac{79}{8}

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

\frac{( x - ( - 1 ) ) ^{2}}{( \frac{79}{4} ) ^{2}} - \frac{( y - ( - \frac{1}{8} ) ) ^{2}}{( \frac{79}{8} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 1, - \frac{1}{8}), a = \frac{79}{4}, b = \frac{79}{8}

x^{2} + 11 = y^{2} + 6 x - 2 y

4 x^{2} - 8 y^{2} + 6 x + 12 y - 82 = 0

x^{2} - y^{2} - 3 x + 4 y = 0

(x - y) (x + y + 6) = - 9

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

What is x^2-4y^2+2x-1y-4=0 ?
The solution to x^2-4y^2+2x-1y-4=0 is Hyperbola with (h,k)=(-1,-1/8),a=(sqrt(79))/4 ,b=(sqrt(79))/8