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Q.

AB is chord of the circle x2+y2=25 whose middle point is M. Then match the following loci of M under various conditions

COLUMN - ICOLUMN - II
A)When AB subtends 60º at centrep)x2+y2+2y=0
B)When AB always passes through (0, –2)q)x2+y2=9
C)When AB has constant length 8r)x2+y2=75/4
D)When AB subtends 45o on the circumference of the circles)2x2+y2=25
 ABCD
1)rpqs
2)sqpr
3)qsrp
4)prsq

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a

2

b

1

c

3

d

4

answer is A.

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Detailed Solution

A) Let M(x1, y1)

cos300=(OM)5x12+y12=2534

 Locus of Mx1,y1 is x2+y2=754

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B) S1 = S11 passes through (0, –2)

C) 2S11=8

D) tan45=OMAM

OM=AM=52OM2=252 locus of x1,y1 is 2x2+y2=25

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