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

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

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5x^2+2y^2=2

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

(h, k) = (0, 0), a = \frac{2}{5}, b = 1

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{2}{5}, b = 1

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 1, a = \frac{2}{5}

3 (x - 5)^{2} + 4 (y + 1)^{2} = 6

- 8 y^{2} + 72 < 9 x^{2}

4 x^{2} + 9 y^{2} + 16 x + 54 y + 61 = 0

4 x^{2} - 16 x + y^{2} + 2 y + 13 = 0

\frac{( x + 3 ) ^{2}}{49} + \frac{( y + 2 ) ^{2}}{21} = 1

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