What is x^2+4y^2-4=0 ?

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

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x^2+4y^2-4=0

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

(h, k) = (0, 0), a = 2, b = 1

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 2, b = 1

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 2, b = 1

4 x^{2} + y^{2} - 16 x + 6 y - 75 = 0

x^{2} + 5 y^{2} - 4 x + 40 y + 64 = 0

4 x^{2} - 24 x + \frac{y ^{2}}{16} + \frac{y}{8} + \frac{573}{16} = 0

\frac{( x + 2 ) ^{2}}{4} + \frac{( y - 7 ) ^{2}}{49} = 1

\frac{( x - 2 ) ^{2}}{64} + \frac{( y + 4 ) ^{2}}{16} = 1

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