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For agtbgtcgt0, the distance between (1 ...

For `agtbgtcgt0`, 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 `2sqrt2`, then

A

`a+b-c gt 0`

B

`a-b+c lt 0`

C

`a-b+c gt0`

D

`a+b-c lt 0`

Text Solution

Verified by Experts

The correct Answer is:
A
Solving given lines for their point of intersection, we get the point of intersection as (-c/(a+b), -c/(a+b)).
Its distance from (1, 1) is
`sqrt((1+(c)/(a+b))^(2) + (1+(c)/(a+b))^(2)) lt 2sqrt(2) " " ("given")`
`"or " (a+b+c)^(2) lt 4(a+b)^(2) " or " (a+b+c)^(2)-(2a+2b)^(2) lt 0`
`"or " (c-a-b)(c+3a+3b) lt 0`
`"Since "a gt b gt c gt 0, (c-a-b) lt 0 " or "a+b-c gt 0`
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