What is 4x^2-y^2+8x-2y+7=0 ?

The solution to 4x^2-y^2+8x-2y+7=0 is Hyperbola with (h,k)=(-1,-1),a=2,b=1

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4x^2-y^2+8x-2y+7=0

4 x^{2} - y^{2} + 8 x - 2 y + 7 = 0

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

Solution steps

4 x^{2} - y^{2} + 8 x - 2 y + 7 = 0

Rewrite

4 x^{2} - y^{2} + 8 x - 2 y + 7 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

x^{2} + 36 y - 32 x - y^{2} = 75

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

y^{2} = x^{2} + 5

x^{2} - 5 y^{2} - 2 x + 20 y = 44

2 x^{2} - 4 y^{2} - 4 x - 8 y = 6

What is 4x^2-y^2+8x-2y+7=0 ?
The solution to 4x^2-y^2+8x-2y+7=0 is Hyperbola with (h,k)=(-1,-1),a=2,b=1