What is x^2+4y^2=e^2 ?

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

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x^2+4y^2=e^2

x^{2} + 4 y^{2} = e^{2}

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

Solution steps

x^{2} + 4 y^{2} = e^{2}

Rewrite

x^{2} + 4 y^{2} = e^{2}

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

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

5 x^{2} + 9 y^{2} - 30 x = 0

\frac{( x + 5 ) ^{2}}{97} + \frac{( y + 2 ) ^{2}}{36} = 1

2 a^{2} + b^{2} = a + b

\frac{( x - 1 ) ^{2}}{16} + \frac{( y - 4 ) ^{2}}{52} = 1

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