What is 4-9x^2-2y^2=0 ?

The solution to 4-9x^2-2y^2=0 is Ellipse with (h,k)=(0,0),a= 2/3 ,b=sqrt(2)

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4-9x^2-2y^2=0

4 - 9 x^{2} - 2 y^{2} = 0

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

Solution steps

4 - 9 x^{2} - 2 y^{2} = 0

Rewrite

4 - 9 x^{2} - 2 y^{2} = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

9 x^{2} + y^{2} + 18 x + 4 y + 4 = 0

4 x^{2} + y^{2} - 16 x - 6 y + 21 = 0

25 x^{2} + 16 y^{2} + 50 x - 64 y - 311 = 0

18 x^{2} + 24 x + 12 y^{2} - 12 y = 1

16 x^{2} + 25 y^{2} - 64 x - 50 y - 311 = 0

What is 4-9x^2-2y^2=0 ?
The solution to 4-9x^2-2y^2=0 is Ellipse with (h,k)=(0,0),a= 2/3 ,b=sqrt(2)