What is x^2+5y^2= 1/2 ?

The solution to x^2+5y^2= 1/2 is Ellipse with (h,k)=(0,0),a=sqrt(1/2),b=sqrt(1/10)

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x^2+5y^2= 1/2

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

(h, k) = (0, 0), a = \frac{1}{2}, b = \frac{1}{10}

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{1}{2} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{1}{10} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{1}{2}, b = \frac{1}{10}

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}{10}

\frac{( x ^{2} )}{9} + \frac{( ( y - 1 ) ^{2} )}{25} = 1

\frac{( y - 2 ) ^{2} + ( x \frac{1}{2} ) ^{2}}{9} = 1

x^{(2)} - 4 x + 3 y^{(2)} = - 2

25 x^{(2)} + 4 y^{(2)} = 84

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

What is x^2+5y^2= 1/2 ?
The solution to x^2+5y^2= 1/2 is Ellipse with (h,k)=(0,0),a=sqrt(1/2),b=sqrt(1/10)