What is 4x^2-8y^2=3 ?

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

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4x^2-8y^2=3

4 x^{2} - 8 y^{2} = 3

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

Solution steps

4 x^{2} - 8 y^{2} = 3

Rewrite

4 x^{2} - 8 y^{2} = 3

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

y^{2} = x^{2} + 9

x^{2} - y^{2} + 2 x - y = 0

y^{2} - 4 y - 4 x^{2} + 8 x - 4 = 0

- 9 x^{2} - 32 y = - 16 y^{2} + 128

x^{2} - 2 x - 4 y^{2} + 24 y = 31

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