What is 36x^2-4y^2-36x-8y=31 ?

The solution to 36x^2-4y^2-36x-8y=31 is Hyperbola with (h,k)=(1/2 ,-1),a=1,b=3

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36x^2-4y^2-36x-8y=31

36 x^{2} - 4 y^{2} - 36 x - 8 y = 31

(h, k) = (\frac{1}{2}, - 1), a = 1, b = 3

Solution steps

36 x^{2} - 4 y^{2} - 36 x - 8 y = 31

Rewrite

36 x^{2} - 4 y^{2} - 36 x - 8 y = 31

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (\frac{1}{2}, - 1), a = 1, b = 3

\frac{( x - 3 ) ^{2}}{16} - \frac{( y - 2 ) ^{2}}{9} = 1

9 x^{2} - 4 y^{2} + 54 x + 16 y + 29 = 0

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

\frac{( y - 0 ) ^{2}}{3 ^{2}} - \frac{( x - 2 ) ^{2}}{4 ^{2}} = 1

\frac{( y + 3 ) ^{2}}{9} - \frac{( x - 2 ) ^{2}}{16} = 1

What is 36x^2-4y^2-36x-8y=31 ?
The solution to 36x^2-4y^2-36x-8y=31 is Hyperbola with (h,k)=(1/2 ,-1),a=1,b=3