What is x^2-10x-4y^2-8y+17=0 ?

The solution to x^2-10x-4y^2-8y+17=0 is Hyperbola with (h,k)=(5,-1),a=2,b=1

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x^2-10x-4y^2-8y+17=0

x^{2} - 10 x - 4 y^{2} - 8 y + 17 = 0

(h, k) = (5, - 1), a = 2, b = 1

Solution steps

x^{2} - 10 x - 4 y^{2} - 8 y + 17 = 0

Rewrite

x^{2} - 10 x - 4 y^{2} - 8 y + 17 = 0

in the form of a standard hyperbola equation

\frac{( x - 5 ) ^{2}}{2 ^{2}} - \frac{( y - ( - 1 ) ) ^{2}}{1 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (5, - 1), a = 2, b = 1

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

9 x^{2} - y^{2} - 36 x - 2 y + 44 = 0

t^{2} = 27 + u^{2}

\frac{x ^{2}}{81} - \frac{y ^{2}}{4} = 1

\frac{x ^{2}}{9} + \frac{8 x}{9} - \frac{y ^{2}}{9} + \frac{8 y}{9} - \frac{1}{81} = 0

What is x^2-10x-4y^2-8y+17=0 ?
The solution to x^2-10x-4y^2-8y+17=0 is Hyperbola with (h,k)=(5,-1),a=2,b=1