What is 9x^2+36=y^2+36x+6y ?

The solution to 9x^2+36=y^2+36x+6y is Hyperbola with (h,k)=(2,-3),a=3,b=1

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9x^2+36=y^2+36x+6y

9 x^{2} + 36 = y^{2} + 36 x + 6 y

(h, k) = (2, - 3), a = 3, b = 1

Solution steps

9 x^{2} + 36 = y^{2} + 36 x + 6 y

Rewrite

9 x^{2} + 36 = y^{2} + 36 x + 6 y

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (2, - 3), a = 3, b = 1

- 4 x^{2} + y^{2} = 36

25 y^{2} - 12 x^{2} - 48 x - 75 y = 0

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

\frac{y ^{2}}{15} - \frac{x ^{2}}{1} = 1

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

What is 9x^2+36=y^2+36x+6y ?
The solution to 9x^2+36=y^2+36x+6y is Hyperbola with (h,k)=(2,-3),a=3,b=1