What is x^2-y^2-4x+8y-21=0 ?

The solution to x^2-y^2-4x+8y-21=0 is Hyperbola with (h,k)=(2,4),a=3,b=3

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x^2-y^2-4x+8y-21=0

x^{2} - y^{2} - 4 x + 8 y - 21 = 0

(h, k) = (2, 4), a = 3, b = 3

Solution steps

x^{2} - y^{2} - 4 x + 8 y - 21 = 0

Rewrite

x^{2} - y^{2} - 4 x + 8 y - 21 = 0

in the form of a standard hyperbola equation

\frac{( x - 2 ) ^{2}}{3 ^{2}} - \frac{( y - 4 ) ^{2}}{3 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (2, 4), a = 3, b = 3

x^{2} - 3 y^{2} - 2 x - 6 y + 7 = 0

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

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

4 x^{2} - 9 (y + 1)^{2} = 36

\frac{( x - 1 ) ^{2}}{9} - \frac{( y - 2 ) ^{2}}{16} = 1

What is x^2-y^2-4x+8y-21=0 ?
The solution to x^2-y^2-4x+8y-21=0 is Hyperbola with (h,k)=(2,4),a=3,b=3