What is (8y)/(1+x^2+y^2)=2 ?

The solution to (8y)/(1+x^2+y^2)=2 is Ellipse with (h,k)=(0,2),a=sqrt(3),b=sqrt(3)

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(8y)/(1+x^2+y^2)=2

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

(h, k) = (0, 2), a = 3, b = 3

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 3 ) ^{2}} + \frac{( y - 2 ) ^{2}}{( 3 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 2), a = 3, b = 3

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 2), b = 3, a = 3

\frac{x ^{2}}{9} + \frac{y ^{2}}{7} = 1

\frac{y ^{2}}{a ^{2}} + \frac{x ^{2}}{b ^{2}} = 1

2 x^{2} + 8 y^{2} = 50

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

3 x^{2} + y^{2} = 6

What is (8y)/(1+x^2+y^2)=2 ?
The solution to (8y)/(1+x^2+y^2)=2 is Ellipse with (h,k)=(0,2),a=sqrt(3),b=sqrt(3)