What is 2x^2+9y^2=1 ?

The solution to 2x^2+9y^2=1 is Ellipse with (h,k)=(0,0),a=sqrt(1/2),b= 1/3

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2x^2+9y^2=1

2 x^{2} + 9 y^{2} = 1

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

Solution steps

2 x^{2} + 9 y^{2} = 1

Rewrite

2 x^{2} + 9 y^{2} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

What is 2x^2+9y^2=1 ?
The solution to 2x^2+9y^2=1 is Ellipse with (h,k)=(0,0),a=sqrt(1/2),b= 1/3