What is 3x^2+2y^2-8=0 ?

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

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3x^2+2y^2-8=0

3 x^{2} + 2 y^{2} - 8 = 0

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

Solution steps

3 x^{2} + 2 y^{2} - 8 = 0

Rewrite

3 x^{2} + 2 y^{2} - 8 = 0

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}

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

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

- 1 = x^{2} + (y - 1)^{2}

\frac{x ^{2} + y ^{2}}{x ^{2} + ( y + 1 ) ^{2}} = 16

200 = \frac{1000}{1 + x ^{2} + y ^{2}}

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