What is 3x^2-y^2-2x-4=0 ?

The solution to 3x^2-y^2-2x-4=0 is Hyperbola with (h,k)=(1/3 ,0),a=(sqrt(13))/3 ,b=sqrt(13/3)

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3x^2-y^2-2x-4=0

3 x^{2} - y^{2} - 2 x - 4 = 0

(h, k) = (\frac{1}{3}, 0), a = \frac{13}{3}, b = \frac{13}{3}

Solution steps

3 x^{2} - y^{2} - 2 x - 4 = 0

Rewrite

3 x^{2} - y^{2} - 2 x - 4 = 0

in the form of a standard hyperbola equation

\frac{( x - \frac{1}{3} ) ^{2}}{( \frac{13}{3} ) ^{2}} - \frac{( y - 0 ) ^{2}}{( \frac{13}{3} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (\frac{1}{3}, 0), a = \frac{13}{3}, b = \frac{13}{3}

27 x^{2} - 36 y^{2} - 216 x - 72 y + 225 = 0

a = a^{2} - b^{2}

\frac{x ^{2}}{8} - \frac{y ^{2}}{64} = 1

2 x 4 x + (- 2) y 4 y = - 200

x = \frac{5 x ^{2} - 5 y ^{2}}{2}

What is 3x^2-y^2-2x-4=0 ?
The solution to 3x^2-y^2-2x-4=0 is Hyperbola with (h,k)=(1/3 ,0),a=(sqrt(13))/3 ,b=sqrt(13/3)