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Question

For a>b>c>0, the distance between (1, 1) and the point of intersection of the lines ax+by+c=0 and bx+ay+c=0 is less than 22. Then,


A

a+bc>0

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B

ab+c<0

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C

ab+c>0

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D

a+bc<0

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Solution

The correct option is A

a+bc>0


As a>b>c>0
ac>0 and b>0
a+bc>0(i)
ab>0 and c>0
a+cb>0(ii)
From Eqs. (i) and (ii), option (b) and (d) are eliminated.
Also, the point of intersection for ax+by+c=0 and bx+ay+c=0
i.e (ca+b,ca+b)
The distance between (1, 1) and (ca+b,ca+b)
i.e. less than 22
(1+ca+b)2+(1+ca+b)2<22(a+b+ca+b)2<22a+b+c<2a+2ba+bc>0
Option (a) is correct.


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