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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

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

6 x^{2} + 7 y^{2} = 6

- 4 y^{2} - 6 y = x^{2}

7 x^{(2)} + 10 y^{(2)} - 56 x + 100 y + 292 = 0

\frac{x ^{2}}{17} + \frac{y ^{2}}{15} = 1

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