What is 3X^2+2Y^2=8 ?

The solution to 3X^2+2Y^2=8 is Ellipse with (h,k)=(0,0),a=(2sqrt(2))/(sqrt(3)),b=2

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3X^2+2Y^2=8

3 X^{2} + 2 Y^{2} = 8

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

Solution steps

3 X^{2} + 2 Y^{2} = 8

Rewrite

3 X^{2} + 2 Y^{2} = 8

in the form of the standard ellipse equation

\frac{( X - 0 ) ^{2}}{( \frac{2 2}{3} ) ^{2}} + \frac{( Y - 0 ) ^{2}}{2 ^{2}} = 1

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

9 x^{2} + 36 y^{2} = 324

5 x^{2} + 9 y^{2} - 20 x - 18 y - 16 = 0

(\frac{( x - 1 )}{6})^{2} + \frac{( y - 3 ) ^{2}}{2} = 1

\frac{( x - 0 ) ^{2}}{20} + \frac{( y - 0 ) ^{2}}{36} = 1

2 x^{2} + 4 y^{2} = 200

What is 3X^2+2Y^2=8 ?
The solution to 3X^2+2Y^2=8 is Ellipse with (h,k)=(0,0),a=(2sqrt(2))/(sqrt(3)),b=2