Misc 9 - Find value of p 3x + y - 2 = 0, px + 2y - 3 = 0

Misc 9 - Chapter 10 Class 11 Straight Lines - Part 2
Misc 9 - Chapter 10 Class 11 Straight Lines - Part 3 Misc 9 - Chapter 10 Class 11 Straight Lines - Part 4

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Transcript

Misc 8 Find the value of p so that the three lines 3x + y – 2 = 0, px + 2y – 3 = 0 and 2x – y – 3 = 0 may intersect at one point. Let lines be 3x + y – 2 = 0 px + 2y – 3 = 0 2x – y – 3 = 0 Three line may intersect at one point Finding point of intersection of line (1) & (3) From (1) 3x + y − 2 = 0 3x + y = 2 y = 2 – 3x Putting value of y in (3) 2x – y − 3 = 0 2x − (2 − 3x) − 3 = 0 2x − 2 + 3x − 3 = 0 5x − 5 = 0 5x = 5 x = 5/5 x = 1 Putting x = 1 in (1) 3x + y – 2 = 0 3(1) + y – 2 = 0 3 + y – 2 = 0 y = 2 − 3 y = −1 Hence point of intersection of line (1) & (3) is (1, −1) Given that line (1), (2) & (3) may intersect at one point Hence point (1, −1) will lie on the 2nd line px + 2y − 3 = 0 i.e. (1, −1) satisfy the equation of line Putting x = 1, & y = −1 in (2) px + 2y − 3 = 0 p(1) + 2( −1) − 3 = 0 p − 2 − 3 = 0 p − 5 = 0 p = 5 Hence, for p = 5 the given lines intersect at one point

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.