What is (x^2}{81}-\frac{y^2)/4 =1 ?

The solution to (x^2}{81}-\frac{y^2)/4 =1 is Hyperbola with (h,k)=(0,0),a=9,b=2

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

\frac{x ^{2}}{81} - \frac{y ^{2}}{4} = 1

(h, k) = (0, 0), a = 9, b = 2

Solution steps

\frac{x ^{2}}{81} - \frac{y ^{2}}{4} = 1

Rewrite

\frac{x ^{2}}{81} - \frac{y ^{2}}{4} = 1

in the form of a standard hyperbola equation

\frac{( x - 0 ) ^{2}}{9 ^{2}} - \frac{( y - 0 ) ^{2}}{2 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, 0), a = 9, b = 2

\frac{x ^{2}}{9} + \frac{8 x}{9} - \frac{y ^{2}}{9} + \frac{8 y}{9} - \frac{1}{81} = 0

x^{2} - y^{2} + 2 > 0

3 x^{2} - 2 y^{2} = 30

3 x^{2} - 2 y^{2} = 36

y^{2} - 9 x^{2} - 36 x - 45 = 0

What is (x^2}{81}-\frac{y^2)/4 =1 ?
The solution to (x^2}{81}-\frac{y^2)/4 =1 is Hyperbola with (h,k)=(0,0),a=9,b=2