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

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

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4x^2+2y^2=1

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

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

Solution steps

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

Rewrite

4 x^{2} + 2 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}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{1}{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} + 9 y^{2}

64 x^{2} + 9 y^{2} = 576

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

(\frac{x}{16})^{2} + (\frac{y}{4})^{2} = 1

x^{2} + 16 y^{2} - 64 = 0

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