What is 4x^2-9y^2=1 ?

The solution to 4x^2-9y^2=1 is Hyperbola with (h,k)=(0,0),a= 1/2 ,b= 1/3

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4x^2-9y^2=1

4 x^{2} - 9 y^{2} = 1

(h, k) = (0, 0), a = \frac{1}{2}, b = \frac{1}{3}

Solution steps

4 x^{2} - 9 y^{2} = 1

Rewrite

4 x^{2} - 9 y^{2} = 1

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (0, 0), a = \frac{1}{2}, b = \frac{1}{3}

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

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

\frac{x ^{2}}{65} - \frac{y ^{2}}{65} = 1

x^{2} - y^{2} + 4 y = 1

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

What is 4x^2-9y^2=1 ?
The solution to 4x^2-9y^2=1 is Hyperbola with (h,k)=(0,0),a= 1/2 ,b= 1/3