What is y^2=(1-4x^2)/5 ?

The solution to y^2=(1-4x^2)/5 is Ellipse with (h,k)=(0,0),a= 1/2 ,b=sqrt(1/5)

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y^2=(1-4x^2)/5

y^{2} = \frac{1 - 4 x ^{2}}{5}

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

Solution steps

y^{2} = \frac{1 - 4 x ^{2}}{5}

Rewrite

y^{2} - \frac{1 - 4 x ^{2}}{5} = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

\frac{( x + 9 ) ^{2}}{81} + \frac{( y - 1 ) ^{2}}{9} = 1

9 x^{2} + 25 y^{2} - 36 x + 50 y - 200 = 0

\frac{( X + 2 ) ^{2}}{4} + \frac{( y - 3 ) ^{2}}{9} = 1

7 x^{2} + 16 y^{2} - 112 = 0

(x - h)^{2} + (y - k)^{2} = 1

What is y^2=(1-4x^2)/5 ?
The solution to y^2=(1-4x^2)/5 is Ellipse with (h,k)=(0,0),a= 1/2 ,b=sqrt(1/5)