What is y^2=4x^2+3x+2 ?

The solution to y^2=4x^2+3x+2 is Hyperbola with (h,k)=(-3/8 ,0),a=(sqrt(23))/4 ,b=(sqrt(23))/8

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y^2=4x^2+3x+2

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

(h, k) = (- \frac{3}{8}, 0), a = \frac{23}{4}, b = \frac{23}{8}

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

\frac{( y - 0 ) ^{2}}{( \frac{23}{4} ) ^{2}} - \frac{( x - ( - \frac{3}{8} ) ) ^{2}}{( \frac{23}{8} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- \frac{3}{8}, 0), a = \frac{23}{4}, b = \frac{23}{8}

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

\frac{v ^{2}}{2} = 2 s^{2} - 0.02

4 x^{2} - 9 y^{2} = 144

x^{2} - 3 y^{2} - 3 x = 4 y + 5

\frac{x ^{2}}{16} - \frac{y ^{2}}{75.9} = 1

What is y^2=4x^2+3x+2 ?
The solution to y^2=4x^2+3x+2 is Hyperbola with (h,k)=(-3/8 ,0),a=(sqrt(23))/4 ,b=(sqrt(23))/8