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

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

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

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

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

Solution steps

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

Rewrite

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

4 x^{2} + y^{2} \leq 4

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

\frac{( y + 1 ) ^{2}}{16} + \frac{x ^{2}}{4} - 1 = 0

\frac{( y - 4 ) ^{2}}{25} + \frac{( x + 2 ) ^{2}}{4} = 1

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

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