1sir can you elaborate a bit more on :-
"z lies on a circle of which z1 and z2 are the ends of a chord" [7]
8 Answers
341Hint: z lies on a circle of which z1 and z2 are the ends of a chord. Can you establish that the centre of this circle is (7,9)?
1341Its not hard to prove that the locus of z is the segment of a circle, with z1 and z2 subtending the angle of 450 on that segment.
That means this chord subtends an angle of 900 at the centre. Also, this centre being equidistant from z1 and z2 will lie on the perpendicular bisector.
So we have two clues: 1. the centre lies on the perpendicular bisector of the line joining z1 and z2 and (2) this point is equidistant from z1 and z2.
There are only two such points. It remains to explain why (7,9) should be chosen among these two.
Thats the task for you guys :)
24(7,9) is chosen because z has arg as π/4
=>Major arc of circle
=>Centre lies above the chord AB
where A=(10,6) B=(4,6).......
24Though the hints of theprophet say it all.........but still I am posting the soln.........