What is 3x^2-2y^2-6x+7y+7=0 ?

The solution to 3x^2-2y^2-6x+7y+7=0 is Hyperbola with (h,k)=(1, 7/4),a= 9/4 ,b=(3sqrt(3))/(2sqrt(2))

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3x^2-2y^2-6x+7y+7=0

3 x^{2} - 2 y^{2} - 6 x + 7 y + 7 = 0

(h, k) = (1, \frac{7}{4}), a = \frac{9}{4}, b = \frac{3 3}{2 2}

Solution steps

3 x^{2} - 2 y^{2} - 6 x + 7 y + 7 = 0

Rewrite

3 x^{2} - 2 y^{2} - 6 x + 7 y + 7 = 0

in the form of a standard hyperbola equation

\frac{( y - \frac{7}{4} ) ^{2}}{( \frac{9}{4} ) ^{2}} - \frac{( x - 1 ) ^{2}}{( \frac{3 3}{2 2} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (1, \frac{7}{4}), a = \frac{9}{4}, b = \frac{3 3}{2 2}

(x - (- 2))^{2} - (y - (- 5))^{2} = (12)^{2}

3 - 4 x + x^{2} - y^{2} \geq 0

y^{2} - 16 x^{2} - 8 y - 96 x - 144 = 0

- \frac{( x + 2 ) ^{2}}{4} + 5 y^{2} = 1

9 x^{2} - 4 y^{2} - 54 x - 40 y - 55 = 0

What is 3x^2-2y^2-6x+7y+7=0 ?
The solution to 3x^2-2y^2-6x+7y+7=0 is Hyperbola with (h,k)=(1, 7/4),a= 9/4 ,b=(3sqrt(3))/(2sqrt(2))