- #1
dj_silver
- 6
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Using converse of alternate segment theorem (i think it is)
i.e. this:
"If the line joining two points A and B subtends equal magnitude angles at two other points on the same side of it, then the four points lie on a circle"
establish the cartesian equation, range and domain of the locus of points:
Arg(z - a) - Arg(z) = pi/2
a = 1 + 0i
and for
Arg(z) - Arg(z-a) = pi/2
a = 1 + 0i
say z = x + iy ( i think )
i get
( x - 1/2 ) ^2 + y^2 = 1/4
But I'm not sure about the domain, range etc
If anyone could help me, or point me in the right direction, that would be great.
Thanks.
i.e. this:
"If the line joining two points A and B subtends equal magnitude angles at two other points on the same side of it, then the four points lie on a circle"
establish the cartesian equation, range and domain of the locus of points:
Arg(z - a) - Arg(z) = pi/2
a = 1 + 0i
and for
Arg(z) - Arg(z-a) = pi/2
a = 1 + 0i
say z = x + iy ( i think )
i get
( x - 1/2 ) ^2 + y^2 = 1/4
But I'm not sure about the domain, range etc
If anyone could help me, or point me in the right direction, that would be great.
Thanks.