Find the conditions that the straight lines y = m1x + c1, y = m2x + c2 and y = m3x + c3 may meet in a point.
Given:
The given lines can be written as follows:
m1x – y + c1 = 0 … (1)
m2x – y + c2 = 0 … (2)
m3x – y + c3 = 0 … (3)
To find:
Conditions that the straight lines y = m1x + c1, y = m2x + c2 and y = m3x + c3 may meet in a point.
Concept Used:
Determinant of equation is zero.
Explanation:
It is given that the three lines are concurrent.
∴ 
⇒ m1(-c3 + c2) + 1(m2c3-m3c2) + c1(-m2 + m3) = 0
⇒ m1(c2-c3) + m2(c3-c1) + m3(c1-c2) = 0
Hence, the required condition is m1(c2-c3) + m2(c3-c1) + m3(c1-c2) = 0
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