x^2+5y^2=2

Solution

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

(h, k) = (0, 0), a = 2, b = \frac{2}{5}

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 2, b = \frac{2}{5}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 2, b = \frac{2}{5}

x^{2} + 4 y^{2} + 2 x + 8 y + 1 = 0

25 x^{2} + 16 y^{2} + 150 x - 128 y - 1119 = 0

\frac{( x - 3 ) ^{2}}{25} + \frac{( y + 2 ) ^{2}}{16} = 1

\frac{x ^{2}}{4} + \frac{y ^{2}}{49} = 1

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

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