What is (1+b+ia)/(1+b-ia)=b+ia ?

The solution to (1+b+ia)/(1+b-ia)=b+ia is Ellipse with (h,k)=(0,0),a=1,b=1

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(1+b+ia)/(1+b-ia)=b+ia

\frac{1 + b + ia}{1 + b - ia} = b + ia

(h, k) = (0, 0), a = 1, b = 1

Solution steps

\frac{1 + b + ia}{1 + b - ia} = b + ia

Rewrite

\frac{1 + b + ia}{1 + b - ia} - b - ia = 0

in the form of the standard ellipse equation

\frac{( b - 0 ) ^{2}}{1 ^{2}} + \frac{( a - 0 ) ^{2}}{1 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 1, 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 = 1

2 x^{2} + y^{2} + 4 x - 6 y - 12 = 0

(\frac{X}{16})^{2} + \frac{( Y + 1 ) ^{2}}{4} - 1 = 0

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

\frac{( x + 2 ) ^{2}}{25} + \frac{( y - 1 ) ^{2}}{9} = 1

25 x^{2} + 16 y^{2} + 100 x - 96 y = 156

What is (1+b+ia)/(1+b-ia)=b+ia ?
The solution to (1+b+ia)/(1+b-ia)=b+ia is Ellipse with (h,k)=(0,0),a=1,b=1