What is 4y^2-3x^2-8y+6x-3=0 ?

The solution to 4y^2-3x^2-8y+6x-3=0 is Hyperbola with (h,k)=(1,1),a=1,b= 2/(sqrt(3))

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4y^2-3x^2-8y+6x-3=0

4 y^{2} - 3 x^{2} - 8 y + 6 x - 3 = 0

(h, k) = (1, 1), a = 1, b = \frac{2}{3}

Solution steps

4 y^{2} - 3 x^{2} - 8 y + 6 x - 3 = 0

Rewrite

4 y^{2} - 3 x^{2} - 8 y + 6 x - 3 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (1, 1), a = 1, b = \frac{2}{3}

- x^{2} + 9 y^{2} + 90 y + 189 = 0

\frac{( x ^{2} )}{625} - \frac{( y ^{2} )}{3600} = 1

\frac{x ^{2}}{16} - (y - 7)^{2} = 1

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

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

What is 4y^2-3x^2-8y+6x-3=0 ?
The solution to 4y^2-3x^2-8y+6x-3=0 is Hyperbola with (h,k)=(1,1),a=1,b= 2/(sqrt(3))