What is 0=16-4x^2-y^2 ?

The solution to 0=16-4x^2-y^2 is Ellipse with (h,k)=(0,0),a=2,b=4

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0=16-4x^2-y^2

0 = 16 - 4 x^{2} - y^{2}

(h, k) = (0, 0), a = 2, b = 4

Solution steps

0 = 16 - 4 x^{2} - y^{2}

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{2 ^{2}} + \frac{( y - 0 ) ^{2}}{4 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 2, b = 4

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 4, a = 2

4 x^{2} + 9 y^{2} + 8 x - 18 y - 23 = 0

x^{2} + 4 y^{2} - 4 x - 32 y + 32 = 0

\frac{( x - 1 ) ^{2}}{5} + \frac{( y + 2 ) ^{2}}{8} = 1

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

\frac{( x - 1 ) ^{2}}{9} + \frac{( y - 5 ) ^{2}}{25} = 1

What is 0=16-4x^2-y^2 ?
The solution to 0=16-4x^2-y^2 is Ellipse with (h,k)=(0,0),a=2,b=4