What is x^2-9y^2=27 ?

The solution to x^2-9y^2=27 is Hyperbola with (h,k)=(0,0),a=3sqrt(3),b=sqrt(3)

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x^2-9y^2=27

x^{2} - 9 y^{2} = 27

(h, k) = (0, 0), a = 33, b = 3

Solution steps

x^{2} - 9 y^{2} = 27

Rewrite

x^{2} - 9 y^{2} = 27

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (0, 0), a = 33, b = 3

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

4 x^{2} = y^{2} + 100

\frac{x ^{2}}{1} - \frac{y ^{2}}{35} = 1

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

x^{2} - y^{2} - 64 = 0

What is x^2-9y^2=27 ?
The solution to x^2-9y^2=27 is Hyperbola with (h,k)=(0,0),a=3sqrt(3),b=sqrt(3)