What is y^2=(4-x^2)/5 ?

The solution to y^2=(4-x^2)/5 is Ellipse with (h,k)=(0,0),a=2,b= 2/(sqrt(5))

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y^2=(4-x^2)/5

y^{2} = \frac{4 - x ^{2}}{5}

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

Solution steps

y^{2} = \frac{4 - x ^{2}}{5}

Rewrite

y^{2} - \frac{4 - x ^{2}}{5} = 0

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}

What is y^2=(4-x^2)/5 ?
The solution to y^2=(4-x^2)/5 is Ellipse with (h,k)=(0,0),a=2,b= 2/(sqrt(5))