Quadratic Equations

Let

z%3Dx%2Bi%20y

%5Ctherefore%20%5Cfrac%7Bz-1%7D%7B2%20z%2B1%7D%3D%5Cfrac%7Bx%2Bi%20y-1%7D%7B2%20x%2B2%20i%20y%2B1%7D

%3D%5Cfrac%7B(x-1)%2Bi%20y%7D%7B(2%20x%2B1)%2B2%20i%20y%7D%20%5Ctimes%20%5Cfrac%7B(2%20x%2B1)-2%20i%20y%7D%7B(2%20x%2B1)-2%20i%20y%7D

%3D%5Cfrac%7B(x-1)(2%20x%2B1)-2%20i%20y(x-1)%2Bi%20y(2%20x%2B1)%2B2%20y%5E%7B2%7D%7D%7B(2%20x%2B1)%5E%7B2%7D%2B4%20y%5E%7B2%7D%7D

%3D%5Cfrac%7B%5Cleft%5C%7B(x-1)(2%20x%2B1)%2B2%20y%5E%7B2%7D%5Cright%5C%7D%2Bi%20y%5C%7B-2%20x%2B2%2B2%20x%2B1%5C%7D%7D%7B(2%20x%2B1)%5E%7B2%7D%2B4%20y%5E%7B2%7D%7D

According to question

I_%7Bm%7D%5Cleft(%5Cfrac%7Bz-1%7D%7B2%20z%2B1%7D%5Cright)%3D-4

%5Ctherefore%20%5Cfrac%7B3%20y%7D%7B(2%20x%2B1)%5E%7B2%7D%2B4%20y%5E%7B2%7D%7D%3D-4

%5CRightarrow-%5Cfrac%7B3%20y%7D%7B4%7D%3D4%20x%5E%7B2%7D%2B4%20y%5E%7B2%7D%2B4%20x%2B1

%5CRightarrow%2016%20x%5E%7B2%7D%2B16%20y%5E%7B2%7D%2B16%20x%2B3%20y%2B4%3D0

This equation represents a circle.

%5Ctherefore

The locus of

z

is a circle.

Chapter Questions
1 MCQs