What is 3x^2-2y^2+32y-134=0 ?

The solution to 3x^2-2y^2+32y-134=0 is Hyperbola with (h,k)=(0,8),a=sqrt(2),b=sqrt(3)

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3x^2-2y^2+32y-134=0

3 x^{2} - 2 y^{2} + 32 y - 134 = 0

(h, k) = (0, 8), a = 2, b = 3

Solution steps

3 x^{2} - 2 y^{2} + 32 y - 134 = 0

Rewrite

3 x^{2} - 2 y^{2} + 32 y - 134 = 0

in the form of a standard hyperbola equation

\frac{( x - 0 ) ^{2}}{( 2 ) ^{2}} - \frac{( y - 8 ) ^{2}}{( 3 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, 8), a = 2, b = 3

4 x^{2} - 9 y^{2} - 16 x + 18 y - 9 = 0

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

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

a^{2} - b^{2} = 68

\frac{x ^{2}}{9} - \frac{y ^{2}}{40} = 1

What is 3x^2-2y^2+32y-134=0 ?
The solution to 3x^2-2y^2+32y-134=0 is Hyperbola with (h,k)=(0,8),a=sqrt(2),b=sqrt(3)