What is (4y^2)/9-(4x^2)/(27)=1 ?

The solution to (4y^2)/9-(4x^2)/(27)=1 is Hyperbola with (h,k)=(0,0),a= 3/2 ,b=(3sqrt(3))/2

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(4y^2)/9-(4x^2)/(27)=1

\frac{4 y ^{2}}{9} - \frac{4 x ^{2}}{27} = 1

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

Solution steps

\frac{4 y ^{2}}{9} - \frac{4 x ^{2}}{27} = 1

Rewrite

\frac{4 y ^{2}}{9} - \frac{4 x ^{2}}{27} = 1

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

2 x^{2} - 3 y^{2} + 8 x + 6 y - 115 = 0

x^{2} - 4 y^{2} = 5

a^{2} - 4 b^{2} = 15

9 x^{2} - 4 y^{2} - 18 x + 8 y + 10 = 0

x^{2} - y^{2} - 4 x + 3 = 0

What is (4y^2)/9-(4x^2)/(27)=1 ?
The solution to (4y^2)/9-(4x^2)/(27)=1 is Hyperbola with (h,k)=(0,0),a= 3/2 ,b=(3sqrt(3))/2