What is -3y^{(2)}-2x^{(2)}=2 ?

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

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-3y^{(2)}-2x^{(2)}=2

- 3 y^{(2)} - 2 x^{(2)} = 2

(h, k) = (0, 0), a = 1, b = \frac{2}{3}

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{1 ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{2}{3} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 1, b = \frac{2}{3}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 1, b = \frac{2}{3}

60 x^{2} + 108 y^{2} = 6480

22 x^{2} + 66 y^{2} + 60 x + 4 y + 9 = 0

2 x^{2} + 2 y^{2} + 36 y = 0

64 x^{2} + 81 y^{2} - 1152 x - 486 y + 729 = 0

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

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