What is 2x^2-5y^2=13 ?

The solution to 2x^2-5y^2=13 is Hyperbola with (h,k)=(0,0),a=sqrt(13/2),b=sqrt(13/5)

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2x^2-5y^2=13

2 x^{2} - 5 y^{2} = 13

(h, k) = (0, 0), a = \frac{13}{2}, b = \frac{13}{5}

Solution steps

2 x^{2} - 5 y^{2} = 13

Rewrite

2 x^{2} - 5 y^{2} = 13

in the form of a standard hyperbola equation

\frac{( x - 0 ) ^{2}}{( \frac{13}{2} ) ^{2}} - \frac{( y - 0 ) ^{2}}{( \frac{13}{5} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, 0), a = \frac{13}{2}, b = \frac{13}{5}

\frac{( x - 2 ) ^{2}}{9} - \frac{( y + 3 ) ^{2}}{27} = 1

9 x^{2} - 4 y^{2} - 36 x = 0

(\frac{y - 4}{16})^{2} - (\frac{x + 3}{36})^{2} = 1

\frac{( y - 3 ) ^{2}}{25} - \frac{( x + 4 ) ^{2}}{36} = 1

- 4 x^{2} + y^{2} = 64

What is 2x^2-5y^2=13 ?
The solution to 2x^2-5y^2=13 is Hyperbola with (h,k)=(0,0),a=sqrt(13/2),b=sqrt(13/5)