What is x^2-y^2+8x-2y+14=0 ?

The solution to x^2-y^2+8x-2y+14=0 is Hyperbola with (h,k)=(-4,-1),a=1,b=1

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x^2-y^2+8x-2y+14=0

x^{2} - y^{2} + 8 x - 2 y + 14 = 0

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

Solution steps

x^{2} - y^{2} + 8 x - 2 y + 14 = 0

Rewrite

x^{2} - y^{2} + 8 x - 2 y + 14 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

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

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

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

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

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

What is x^2-y^2+8x-2y+14=0 ?
The solution to x^2-y^2+8x-2y+14=0 is Hyperbola with (h,k)=(-4,-1),a=1,b=1