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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

x^{2} + 2 y^{2} - 6 x + 4 y + 7 = 0

9 x^{2} + 16 y^{2} + 36 x - 160 y + 292 = 0

4 x^{2} + 9 y^{2} + 16 x - 54 y + 61 = 0

\frac{( x + 1 ) ^{2}}{16} + \frac{( y - 2 ) ^{2}}{25} = 1

\frac{x ^{2}}{\frac{81}{4}} + \frac{y ^{2}}{\frac{25}{16}} = 1

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