for the third answer...if u r considering B to be the intersection of circle with the y axis, then locus of B will be y axis itself....i think so!!!
1. Two rods of lengths a and b side along coordinate axis in a manner that their ends are always concyclic. Find the locus of the centre of the circle passing throw these ends.
2.The base of a triangle passes throw a fixed point (a,b)and its sides are respectively bisected at right angles by the lines y2 - 8xy - 9x2 = 0.Prove that the locus of the vertex is a circle.Find its equation.
3.A circle of radius r passes through the origin O and cuts the axes A and B.Let p be the foot of perpendicular from the origin to line AB.Find the locus of B.
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5 Answers
The x coordinates be (h,0) and (h+a,0)
The y coordinates be (0,k) and (0,k+b)
The center of the circle will be (h+a/2, k+b/2) (Think why!)
Now the distance from the center will be equal from all points hence
(a/2)2+(k+b/2)2 = (h+a/2)2+(b/2)2
or k2+bk=h2+ah
Now can you finish it off?
@nishant bhaiya....is it that rods r placed like "+" position??...perpendicular to each other intersecting at centres of each other??
no not like that..
but the center of the circle will be lying on the perpendicular bisector of the two lines....