What is 2a-3b^2=4a^2-9b^2 ?

The solution to 2a-3b^2=4a^2-9b^2 is Hyperbola with (h,k)=(1/4 ,0),a= 1/4 ,b= 1/(2sqrt(6))

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2a-3b^2=4a^2-9b^2

2 a - 3 b^{2} = 4 a^{2} - 9 b^{2}

(h, k) = (\frac{1}{4}, 0), a = \frac{1}{4}, b = \frac{1}{2 6}

Solution steps

2 a - 3 b^{2} = 4 a^{2} - 9 b^{2}

Rewrite

2 a - 3 b^{2} - 4 a^{2} + 9 b^{2} = 0

in the form of a standard hyperbola equation

\frac{( a - \frac{1}{4} ) ^{2}}{( \frac{1}{4} ) ^{2}} - \frac{( b - 0 ) ^{2}}{( \frac{1}{2 6} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (\frac{1}{4}, 0), a = \frac{1}{4}, b = \frac{1}{2 6}

\frac{( y - 4 ) ^{2}}{9} - \frac{( x - 2 ) ^{2}}{16} = 1

9 x^{2} - 36 x - y^{2} - 6 y + 18 = 0

x^{2} - y^{2} - y + 9 = 0

16 x^{2} - 9 y^{2} - 96 x + 36 y - 36 = 0

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

What is 2a-3b^2=4a^2-9b^2 ?
The solution to 2a-3b^2=4a^2-9b^2 is Hyperbola with (h,k)=(1/4 ,0),a= 1/4 ,b= 1/(2sqrt(6))