Q. 125.0( 2 Votes )
If a + b + c = 0, then the family of lines 3ax + by + 2c = 0 pass through fixed point
A. (2. 2/3)
B. (2/3, 2)
C. (-2, 2/3)
D. none of these
Answer :
Given:
a + b + c = 0
Substituting c = − a − b in 3ax + by + 2c = 0, we get:
3ax + by – 2a – 2b = 0
⇒ a (3x – 2) + b (y – 2) = 0
This line is of the form L1 + λL2 = 0,
which passes through the intersection of the lines L1 and L2, i.e. 3x – 2 = 0 and y – 2 = 0 .
Solving 3 x – 2 = 0 and y – 2 = 0, we get:
Hence, the required fixed point is
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If a + b + c = 0, then the family of lines 3ax + by + 2c = 0 pass through fixed point
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