What is 3x^2+2x+92=3y^2 ?

The solution to 3x^2+2x+92=3y^2 is Hyperbola with (h,k)=(-1/3 ,0),a=(5sqrt(11))/3 ,b=(5sqrt(11))/3

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3x^2+2x+92=3y^2

3 x^{2} + 2 x + 92 = 3 y^{2}

(h, k) = (- \frac{1}{3}, 0), a = \frac{5 11}{3}, b = \frac{5 11}{3}

Solution steps

3 x^{2} + 2 x + 92 = 3 y^{2}

Rewrite

3 x^{2} + 2 x + 92 = 3 y^{2}

in the form of a standard hyperbola equation

\frac{( y - 0 ) ^{2}}{( \frac{5 11}{3} ) ^{2}} - \frac{( x - ( - \frac{1}{3} ) ) ^{2}}{( \frac{5 11}{3} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- \frac{1}{3}, 0), a = \frac{5 11}{3}, b = \frac{5 11}{3}

4 x^{2} - 4 y^{2} = 64

y^{2} + 2 = 7 x^{2}

4 x^{2} - 25 y^{2} + 48 x + 150 y - 181 = 0

\frac{( x + 6 ) ^{2}}{32} - \frac{( y - 0.25 ) ^{2}}{100} = 1

x^{2} = y^{2} - 13 + 14 x

What is 3x^2+2x+92=3y^2 ?
The solution to 3x^2+2x+92=3y^2 is Hyperbola with (h,k)=(-1/3 ,0),a=(5sqrt(11))/3 ,b=(5sqrt(11))/3