What is 2x^2-3y^2=9 ?

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

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2x^2-3y^2=9

2 x^{2} - 3 y^{2} = 9

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

Solution steps

2 x^{2} - 3 y^{2} = 9

Rewrite

2 x^{2} - 3 y^{2} = 9

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

\frac{x ^{2}}{25} - \frac{y ^{2}}{100} = 1

d^{2} = (3 - 20 t)^{2} + (4 - 30 t)^{2}

x^{2} - y^{2} - 4 x - 6 y - 14 = 0

x^{2} - y^{2} - 6 x + 16 y - 119 = 0

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

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