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

9 x^{2} - y^{2} + 54 x + 10 y + 55 = 0

4 x^{(2)} - 25 y^{(2)} + 16 x + 50 y - 109 = 0

x^{2} + 12 = y^{2} + 6 x - 2 y

- 36 x^{2} + 25 y^{2} = 900

\frac{y ^{2}}{12} - \frac{x ^{2}}{4} = 1

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