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

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

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

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

(h, k) = (0, 0), a = \frac{1}{5}, b = \frac{1}{5}

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{1}{5} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{1}{5} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{1}{5}, b = \frac{1}{5}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = \frac{1}{5}, b = \frac{1}{5}

3 x^{2} + 12 y^{2} + 18 x - 24 y - 69 = 0

x^{2} + y^{2} = - 8 y

3 y^{2} + 5 x^{2} = 20

\frac{( x - 4 ) ^{2}}{36} + \frac{( y - 2 ) ^{2}}{20} = 1

\frac{x ^{2}}{16} + \frac{y ^{2}}{8} = 1

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