What is X^2-Y^2-12=0 ?

The solution to X^2-Y^2-12=0 is Hyperbola with (h,k)=(0,0),a=2sqrt(3),b=2sqrt(3)

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X^2-Y^2-12=0

X^{2} - Y^{2} - 12 = 0

(h, k) = (0, 0), a = 23, b = 23

Solution steps

X^{2} - Y^{2} - 12 = 0

Rewrite

X^{2} - Y^{2} - 12 = 0

in the form of a standard hyperbola equation

\frac{( X - 0 ) ^{2}}{( 2 3 ) ^{2}} - \frac{( Y - 0 ) ^{2}}{( 2 3 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, 0), a = 23, b = 23

(x^{2} - y^{2}) = 23

8 y^{2} + 3 y - 9 = 8 x^{2} + 9 x - 3

\frac{y ^{2}}{6} - \frac{x ^{2}}{9} = 1

y^{2} = 2 x^{2} + 1

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

What is X^2-Y^2-12=0 ?
The solution to X^2-Y^2-12=0 is Hyperbola with (h,k)=(0,0),a=2sqrt(3),b=2sqrt(3)