x^2-2y^2=3

Solution

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

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

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

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

x^{2} - 20 x - 4 y^{2} - 64 y - 172 = 0

5 x^{2} - 4 y^{2} = 20

x^{2} + (y - 5) = (y + 5)^{2}

2 x^{2} - 4 y^{2} = 3

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