What is 1/2 x^2+1/8 y^2= 1/4 ?

The solution to 1/2 x^2+1/8 y^2= 1/4 is Ellipse with (h,k)=(0,0),a=sqrt(1/2),b=sqrt(2)

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1/2 x^2+1/8 y^2= 1/4

\frac{1}{2} x^{2} + \frac{1}{8} y^{2} = \frac{1}{4}

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

Solution steps

\frac{1}{2} x^{2} + \frac{1}{8} y^{2} = \frac{1}{4}

Rewrite

\frac{1}{2} x^{2} + \frac{1}{8} y^{2} = \frac{1}{4}

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

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

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

16 x^{2} + 4 y^{2} - 128 x - 16 y + 206 = 0

2 x^{2} + 6 y^{2} = 168

x^{2} + 25 y^{2} = 1

What is 1/2 x^2+1/8 y^2= 1/4 ?
The solution to 1/2 x^2+1/8 y^2= 1/4 is Ellipse with (h,k)=(0,0),a=sqrt(1/2),b=sqrt(2)