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Question: Answered & Verified by Expert
Let a0, b0, c be three real numbers and Lp,q=ap+bq+ca2+b2,  p, qR. If L23,13+L13,23+L(2,2)=0, then the line ax+by+c=0 always passes through the fixed point
MathematicsStraight LinesTS EAMCETTS EAMCET 2018 (04 May Shift 1)
Options:
  • A 0,1
  • B 1,1
  • C 2,2
  • D -1,-1
Solution:
1504 Upvotes Verified Answer
The correct answer is: 1,1

Given that Lp,q=ap+bq+ca2+b2.

L23,13=a23+b13+ca2+b2=2a+b+3c3a2+b2

L13,23=a13+b23+ca2+b2=a+2b+3c3a2+b2

L2,2=a2+b2+ca2+b2=2a+2b+ca2+b2=6a+6b+3c3a2+b2

L23,13+L13,23+L2,2

=2a+b+3c3a2+b2+a+2b+3c3a2+b2+6a+6b+3c3a2+b2

=9a+9b+9c3a2+b2=0

 9a+9b+9c=0a+b+c=0   ...1

By verifying the options

Substitute (1,1) in the given equation of line,

a1+b1+c=0    ...2

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