What is 3x^2+2y^2=1 ?

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

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3x^2+2y^2=1

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

25 y^{2} + 4 x^{2} - 250 y - 16 x + 541 = 0

2 x^{2} - 8 x + y^{2} - 10 y = 60

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

2 x^{2} + 2 y^{2} - 36 y = 0

\frac{x ^{2}}{8 0 ^{2}} + \frac{y ^{2}}{62. 5 ^{2}} = 1

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