Q.

Let the circle (x1)2+(y2)2=25 cuts a rectangular hyperbola with transverse axis along  y=xat four points A,B,C and D  having coordinates (xi,yi),i=1,2,3,4respectively. O being the center of the hyperbola. Now match the entries from the following two columns

 Column–I Column–II

A

x1+x2+x3+x4 is equal to

P

2

B

x12+x22+x32+x42 is equal to

Q

4

C

OA2+OB2+OC2+OD2 is equal to

R

44

D

y12+y22+y32+y42is equal to

S

56

 

 

T

100

 

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a

AP,BR,CT,DS

b

AP,BQ,CR,DS

c

AP,BT,CQ,DS

d

AS,BQ,CR,DP

answer is C.

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Detailed Solution

x2+y22x4y20=0(1)

xy=c2(2)

P.I of(1)&(2)isP(ct,ct)

c2t42ct320t24ct+c2=0

A)  x1+x2+x3+x4=c(t1+t2+t3+t4)=2

B)​​​x12=(x1)22x1x2=44

C)   (x12+y12)=44+56=100

D)​​ y1=c(1t1+1t2+1t3+1t4)=4

y1y2=c21t1t2=20

y12=(y1)22y1y2=56

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