1wat about other question
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
62The 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?
1@nishant bhaiya....is it that rods r placed like "+" position??...perpendicular to each other intersecting at centres of each other??
1for 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!!!
62no not like that..
but the center of the circle will be lying on the perpendicular bisector of the two lines....