What is 2x^2+5y^2=8 ?

The solution to 2x^2+5y^2=8 is Ellipse with (h,k)=(0,0),a=2,b=(2sqrt(2))/(sqrt(5))

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2x^2+5y^2=8

2 x^{2} + 5 y^{2} = 8

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

Solution steps

2 x^{2} + 5 y^{2} = 8

Rewrite

2 x^{2} + 5 y^{2} = 8

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

\frac{y ^{2}}{81} + \frac{( x + 5 ) ^{2}}{27} = 1

x^{2} + 10 x + 3 y^{2} + 10 y = 14

\frac{x ^{2}}{12} + \frac{y ^{2}}{12 - 16} = 1

22 x^{2} + 4 y^{2} = 1

x^{2} + 4 y^{2} + 10 x + 9 y - 10 = 0

What is 2x^2+5y^2=8 ?
The solution to 2x^2+5y^2=8 is Ellipse with (h,k)=(0,0),a=2,b=(2sqrt(2))/(sqrt(5))