What is 2x^2-3y^2=15 ?

The solution to 2x^2-3y^2=15 is Hyperbola with (h,k)=(0,0),a=sqrt(15/2),b=sqrt(5)

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2x^2-3y^2=15

2 x^{2} - 3 y^{2} = 15

(h, k) = (0, 0), a = \frac{15}{2}, b = 5

Solution steps

2 x^{2} - 3 y^{2} = 15

Rewrite

2 x^{2} - 3 y^{2} = 15

in the form of a standard hyperbola equation

\frac{( x - 0 ) ^{2}}{( \frac{15}{2} ) ^{2}} - \frac{( y - 0 ) ^{2}}{( 5 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, 0), a = \frac{15}{2}, b = 5

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

(x - 9)^{2} - 9 (y + 7)^{2} = 1

4 x^{2} - 9 y^{2} + 24 x - 36 y - 36 = 0

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

\frac{x ^{2}}{25} - \frac{y ^{2}}{121} = 1

What is 2x^2-3y^2=15 ?
The solution to 2x^2-3y^2=15 is Hyperbola with (h,k)=(0,0),a=sqrt(15/2),b=sqrt(5)