What is ((x-3)^2)/(36)-((y-4)^2)/(81)=1 ?

The solution to ((x-3)^2)/(36)-((y-4)^2)/(81)=1 is Hyperbola with (h,k)=(3,4),a=6,b=9

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((x-3)^2)/(36)-((y-4)^2)/(81)=1

\frac{( x - 3 ) ^{2}}{36} - \frac{( y - 4 ) ^{2}}{81} = 1

(h, k) = (3, 4), a = 6, b = 9

Solution steps

\frac{( x - 3 ) ^{2}}{36} - \frac{( y - 4 ) ^{2}}{81} = 1

Rewrite

\frac{( x - 3 ) ^{2}}{36} - \frac{( y - 4 ) ^{2}}{81} = 1

in the form of a standard hyperbola equation

\frac{( x - 3 ) ^{2}}{6 ^{2}} - \frac{( y - 4 ) ^{2}}{9 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (3, 4), a = 6, b = 9

x^{2} - 2 x - y^{2} + 4 y = 7

y^{2} = x^{2} - 8

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

4 x^{2} - y^{2} + 8 x - 2 y + 7 = 0

x^{2} + 36 y - 32 x - y^{2} = 75

What is ((x-3)^2)/(36)-((y-4)^2)/(81)=1 ?
The solution to ((x-3)^2)/(36)-((y-4)^2)/(81)=1 is Hyperbola with (h,k)=(3,4),a=6,b=9