What is a^2-b^2-4a+2b=19 ?

The solution to a^2-b^2-4a+2b=19 is Hyperbola with (h,k)=(2,1),a=sqrt(22),b=sqrt(22)

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a^2-b^2-4a+2b=19

a^{2} - b^{2} - 4 a + 2 b = 19

(h, k) = (2, 1), a = 22, b = 22

Solution steps

a^{2} - b^{2} - 4 a + 2 b = 19

Rewrite

a^{2} - b^{2} - 4 a + 2 b = 19

in the form of a standard hyperbola equation

\frac{( a - 2 ) ^{2}}{( 22 ) ^{2}} - \frac{( b - 1 ) ^{2}}{( 22 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (2, 1), a = 22, b = 22

y^{2} + 1 = x^{2} + 8 x

9 x^{2} - y^{2} = 1

5 x^{2} - 5 y^{2} + 20 x - 60 y = 185

\frac{x ^{2}}{9} - \frac{y ^{2}}{1} = 1

x^{2} - 5 y^{2} = 3 y

What is a^2-b^2-4a+2b=19 ?
The solution to a^2-b^2-4a+2b=19 is Hyperbola with (h,k)=(2,1),a=sqrt(22),b=sqrt(22)