# Misc 8 - Chapter 9 Class 11 Straight Lines

Last updated at April 16, 2024 by Teachoo

Miscellaneous

Misc 1
Important

Misc 2 Important

Misc 3

Misc 4

Misc 5 Important

Misc 6

Misc 7 Important

Misc 8 Important You are here

Misc 9

Misc 10 Important

Misc 11 Important

Misc 12

Misc 13

Misc 14 Important

Misc 15 Important

Misc 16

Misc 17 Important

Misc 18 Important

Misc 19 Important

Misc 20 Important

Misc 21 Important

Misc 22

Misc 23 Important

Question 1 Important

Last updated at April 16, 2024 by Teachoo

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