What is x^2-y^2-4y=1 ?

The solution to x^2-y^2-4y=1 is Hyperbola with (h,k)=(0,-2),a=sqrt(3),b=sqrt(3)

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x^2-y^2-4y=1

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

(h, k) = (0, - 2), a = 3, b = 3

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

\frac{( y - ( - 2 ) ) ^{2}}{( 3 ) ^{2}} - \frac{( x - 0 ) ^{2}}{( 3 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, - 2), a = 3, b = 3

x^{2} - 4 y^{2} - 10 x - 40 y - 100 = 0

3 x^{2} + 6 x = 0.3 y^{2} - 6 y

x^{2} - y^{2} = 45

\frac{x ^{2}}{16} - \frac{y ^{2}}{81} = 1

x^{2} - 9 y^{2} + 8 x + 36 y - 29 = 0

What is x^2-y^2-4y=1 ?
The solution to x^2-y^2-4y=1 is Hyperbola with (h,k)=(0,-2),a=sqrt(3),b=sqrt(3)