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

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

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2x^2+3y^2=1

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

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

Solution steps

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

Rewrite

2 x^{2} + 3 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}

\frac{( x - h ) ^{2}}{a ^{2}} + \frac{( y + k ) ^{2}}{b ^{2}} = 1

(x - 3)^{2} + \frac{y ^{2}}{4} = 1

3 x^{2} + y^{2} = 84

x^{2} + 25 y^{2} - 4 x = 21

\frac{( x + 2 ) ^{2}}{25} + \frac{( y - 4 ) ^{2}}{4} = 1

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