What is (x^2}{16}+\frac{y^2)/4 =1 ?

The solution to (x^2}{16}+\frac{y^2)/4 =1 is Ellipse with (h,k)=(0,0),a=4,b=2

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

\frac{x ^{2}}{16} + \frac{y ^{2}}{4} = 1

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

Solution steps

\frac{x ^{2}}{16} + \frac{y ^{2}}{4} = 1

Rewrite

\frac{x ^{2}}{16} + \frac{y ^{2}}{4} = 1

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

x^{2} = - 4 y

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

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

\frac{x ^{2}}{9} - \frac{y ^{2}}{4} = 1

\frac{y ^{2}}{36} - \frac{x ^{2}}{64} = 1

What is (x^2}{16}+\frac{y^2)/4 =1 ?
The solution to (x^2}{16}+\frac{y^2)/4 =1 is Ellipse with (h,k)=(0,0),a=4,b=2