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

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

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

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

(h, k) = (0, 0), a = \frac{1}{2}, b = 1

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{1}{2}, b = 1

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 1, a = \frac{1}{2}

- x^{2} - \frac{y ^{2}}{49} = 1

\frac{( x + 7 ) ^{2}}{144} + \frac{( y + 2 ) ^{2}}{100} = 1

\frac{x ^{2}}{36} + \frac{( y + 9 ) ^{2}}{81} = 1

4 x^{2} + 18 y^{2} = 36

(x - 3)^{2} + \frac{( y + 1 ) ^{2}}{49} = 1

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