General Equation Of A Circle
Complex Numbers of Class 11
General Equation of A Circle
Let us consider a circle with center at C(z0) with radius r and P any point on the circle.
Then PC = r = |z −z0|
⇒ |z − z0|2 = r2 ⇒ (z − z0)
= r2
⇒ 
⇒ 
where a = 
is real and α = − z0
The center of the circle is −α and radius = 
Circle described on the line segment joining z1 and z2 as diameter is
|
(z − z1)
Clearly ∠APB =
∴ arg
∴ |
|
+ (z − z2) 
= 0
= 
is purely imaginary.
.
|
Condition for the four points z1, z2, z3 and z4 to be concyclic is
is real Let the points A(z1) B(z2) C(z3) and D(z4) be concylic |
|
Then ∠ACB and ∠ADB are either equal or different by π
So arg 
is either O or π.
i.e. 
is real
