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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (1, - 1), b = \frac{7}{2}, a = \frac{7}{3}

9 x^{(2)} + 25 y^{(2)} + 18 x + 150 y + 9 = 0

\frac{y ^{2}}{4} + \frac{x ^{2}}{9} = 1

9 x^{2} + 25 y^{2} + 36 x - 200 y + 211 = 0

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

4 x^{2} + 6 y^{2} - 8 x + 4 y - 6 \geq 0

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