two rods of length a and b slide one along the x axis and the other along y axis is such a manner that their ends are concyclic find the locus of the centre of the circle
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ANSWER
Let (h,k) be the centre of circle of radius r which intersects the axes. Then y intercept of circle (y−k)
2
+(x−h)
2
=r
2
is
y=k±
r
2
−h
2
x intercept x=h±
r
2
−k
2
Length of rod b is b=2
r
2
−h
2
=y
1
−y
2
Similarly length of rod a is a=2
r
2
−k
2
=x
1
−x
2
b
2
+4h
2
=a
2
+4k
2
=4r
2
4(h
2
−k
2
)=(a
2
−b
2
)
h
2
−k
2
=
4
a
2
−b
2
x
2
−y
2
=
4
a
2
−b
2
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