circles- A das gupta (locus)

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.

5 Answers

62
Lokesh Verma ·

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?

1
buddyboyyash ·

@nishant bhaiya....is it that rods r placed like "+" position??...perpendicular to each other intersecting at centres of each other??

1
buddyboyyash ·

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!!!

62
Lokesh Verma ·

no not like that..

but the center of the circle will be lying on the perpendicular bisector of the two lines....

1
jangra28192manoj jangra ·

wat about other question

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