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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

25 x^{2} + 4 y^{2} - 200 x + 24 y + 376 = 0

\frac{( x + 2 ) ^{2}}{9} + \frac{( y + 3 ) ^{2}}{25} = 1

x^{2} + y^{2} - 2 y > 0

\frac{( x - 1 ) ^{2}}{4} + \frac{( y + 3 ) ^{2}}{16} = 1

\frac{x ^{2}}{C _{1}} = 1 - \frac{y ^{2}}{C _{2}}

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