What is x^2-4y^2-20x-64y-172=0 ?

The solution to x^2-4y^2-20x-64y-172=0 is Hyperbola with (h,k)=(10,-8),a=4,b=2

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x^2-4y^2-20x-64y-172=0

x^{2} - 4 y^{2} - 20 x - 64 y - 172 = 0

(h, k) = (10, - 8), a = 4, b = 2

Solution steps

x^{2} - 4 y^{2} - 20 x - 64 y - 172 = 0

Rewrite

x^{2} - 4 y^{2} - 20 x - 64 y - 172 = 0

in the form of a standard hyperbola equation

\frac{( x - 10 ) ^{2}}{4 ^{2}} - \frac{( y - ( - 8 ) ) ^{2}}{2 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (10, - 8), a = 4, b = 2

9 x^{2} + 4 y^{2} - 18 x + 8 y - 23 = 0

25 x^{2} + 4 y^{2} = 100

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

\frac{x ^{2}}{9} + \frac{y ^{2}}{16} = 1

x^{2} - y^{2} = 25

What is x^2-4y^2-20x-64y-172=0 ?
The solution to x^2-4y^2-20x-64y-172=0 is Hyperbola with (h,k)=(10,-8),a=4,b=2