What is 9x^2-72x-4y^2-40y+44=36 ?

The solution to 9x^2-72x-4y^2-40y+44=36 is Hyperbola with (h,k)=(4,-5),a=2,b=3

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9x^2-72x-4y^2-40y+44=36

9 x^{2} - 72 x - 4 y^{2} - 40 y + 44 = 36

(h, k) = (4, - 5), a = 2, b = 3

Solution steps

9 x^{2} - 72 x - 4 y^{2} - 40 y + 44 = 36

Rewrite

9 x^{2} - 72 x - 4 y^{2} - 40 y + 44 = 36

in the form of a standard hyperbola equation

\frac{( x - 4 ) ^{2}}{2 ^{2}} - \frac{( y - ( - 5 ) ) ^{2}}{3 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (4, - 5), a = 2, b = 3

4 x^{2} + 24 x - 2 y^{2} + 36 = 36

\frac{( y - 3 ) ^{2}}{4} - \frac{( x + 1 ) ^{2}}{16} = 1

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

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

4 x^{2} - 24 x - y^{2} - 2 y = - 31

What is 9x^2-72x-4y^2-40y+44=36 ?
The solution to 9x^2-72x-4y^2-40y+44=36 is Hyperbola with (h,k)=(4,-5),a=2,b=3