What is 3x^2-4y^2+3-6x+16y-18=0 ?

The solution to 3x^2-4y^2+3-6x+16y-18=0 is Hyperbola with (h,k)=(1,2),a=sqrt(2/3),b=sqrt(1/2)

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3x^2-4y^2+3-6x+16y-18=0

3 x^{2} - 4 y^{2} + 3 - 6 x + 16 y - 18 = 0

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

Solution steps

3 x^{2} - 4 y^{2} + 3 - 6 x + 16 y - 18 = 0

Rewrite

3 x^{2} - 4 y^{2} + 3 - 6 x + 16 y - 18 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

\frac{y ^{2}}{625} - \frac{x ^{2}}{2500} = 1

x^{2} - y^{2} = - 16

- x^{2} + 2 x + 4 y^{2} + 24 y + 31 = 0

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

(x + y) (x - y) = 119

What is 3x^2-4y^2+3-6x+16y-18=0 ?
The solution to 3x^2-4y^2+3-6x+16y-18=0 is Hyperbola with (h,k)=(1,2),a=sqrt(2/3),b=sqrt(1/2)