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

The solution to (8x)/(x^2+y^2+1)=1 is Ellipse with (h,k)=(4,0),a=sqrt(15),b=sqrt(15)

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

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

(h, k) = (4, 0), a = 15, b = 15

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - 4 ) ^{2}}{( 15 ) ^{2}} + \frac{( y - 0 ) ^{2}}{( 15 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (4, 0), a = 15, b = 15

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (4, 0), b = 15, a = 15

(16 - x^{2} - 9 y^{2}) = - 1

36 x^{2} + 17 y^{2} - 648 x + 238 y + 689 = 0

25 x^{2} + 16 y^{2} - 200 x - 160 y + 400 = 0

\frac{x ^{2}}{64} + \frac{( y - 6 ) ^{2}}{121} = 1

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

What is (8x)/(x^2+y^2+1)=1 ?
The solution to (8x)/(x^2+y^2+1)=1 is Ellipse with (h,k)=(4,0),a=sqrt(15),b=sqrt(15)