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

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

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3y^2=-2x^2+1

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

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

Solution steps

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

Rewrite

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

12 x^{2} + 16 y^{2} = 192

\frac{x ^{2}}{c _{1}^{2}} = 1 - \frac{y ^{2}}{c _{2}^{2}}

16 x^{2} + 4 y^{2} - 32 x + 24 y - 12 = 0

x^{2} - 2 x + \frac{y ^{2}}{4} - y \leq 14

x^{2} + 3 y^{2} = 6

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