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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

\frac{( x - 3 ) ^{2}}{10} - \frac{( y + 5 ) ^{2}}{9} = 4

x, 12 Y (x)^{2} - 15 x^{2} = 180

9 x^{2} - 16 y^{2} - 90 x - 96 y - 63 = 0

\frac{y ^{2}}{4} - (x + 2)^{2} = 1

x^{2} - 9 (y + 1)^{2} - 9 = x + 2 y + 5

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