Misc 9 - Chapter 10 Class 11 Straight Lines

Transcript

Misc 9 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