1.

Find the value of P if the straight lines x + P = 0, y + 2 = 0, 3x + 2y + 5 = 0 are concurrent.

Answer»

Given straight line equations are

x + P = 0   ...... (1)

y + 2 = 0 ⇒ y = –2  ...... (2)

3x + 2y + 5 = 0  ....... (3)

Solving (2) & (3)

3x + 2(–2) + 5 = 0

⇒ 3x + 1 = 0

⇒ x = −1/3

Point of intersection of (2) & (3) is  (−1/3, - 2)

Since (1), (2), (3) are concurrent

This point lies on (1)

⇒ −1/3 + P = 0

⇒ P = 1/3



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