What is 3x^2+4y^2= 1/2 ?

The solution to 3x^2+4y^2= 1/2 is Ellipse with (h,k)=(0,0),a=sqrt(1/6),b= 1/(2sqrt(2))

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3x^2+4y^2= 1/2

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

(h, k) = (0, 0), a = \frac{1}{6}, b = \frac{1}{2 2}

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{1}{6} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{1}{2 2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{1}{6}, b = \frac{1}{2 2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = \frac{1}{6}, b = \frac{1}{2 2}

5 x^{2} + 9 y^{2} - 10 x + 4 = 0

3 x^{(2)} + y^{(2)} - 24 x + 39 = 0

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

(x - 2)^{2} + (y + 1)^{2} = 5 - 5 y^{2}

9 (x - 1)^{2} + (4 y)^{2} = 36

What is 3x^2+4y^2= 1/2 ?
The solution to 3x^2+4y^2= 1/2 is Ellipse with (h,k)=(0,0),a=sqrt(1/6),b= 1/(2sqrt(2))