What is 2x^2-3y^2=47 ?

The solution to 2x^2-3y^2=47 is Hyperbola with (h,k)=(0,0),a=sqrt(47/2),b=sqrt(47/3)

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2x^2-3y^2=47

2 x^{2} - 3 y^{2} = 47

(h, k) = (0, 0), a = \frac{47}{2}, b = \frac{47}{3}

Solution steps

2 x^{2} - 3 y^{2} = 47

Rewrite

2 x^{2} - 3 y^{2} = 47

in the form of a standard hyperbola equation

\frac{( x - 0 ) ^{2}}{( \frac{47}{2} ) ^{2}} - \frac{( y - 0 ) ^{2}}{( \frac{47}{3} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, 0), a = \frac{47}{2}, b = \frac{47}{3}

- 9 x^{2} + 4 y^{2} = 144

\frac{( x + 3 ) ^{2}}{9} - \frac{( y - 4 ) ^{2}}{16} = 1

y^{2} = \frac{16 - x ^{2}}{- 4}

(\frac{x + 1}{36})^{2} - (\frac{y - 4}{64})^{2} = 1

\frac{( x - 3 ) ^{2}}{36} - \frac{( y - 2 ) ^{2}}{64} = 1

What is 2x^2-3y^2=47 ?
The solution to 2x^2-3y^2=47 is Hyperbola with (h,k)=(0,0),a=sqrt(47/2),b=sqrt(47/3)