Example 20 - Chapter 10 Class 11 Straight Lines (Term 1)
Last updated at Feb. 3, 2020 by Teachoo
Last updated at Feb. 3, 2020 by Teachoo
Transcript
Example 20 If the lines 2x + y – 3 = 0, 5x + ky – 3 = 0 and 3x – y – 2 = 0 are concurrent, find the value of k. Three lines are concurrent if they pass through a common point i.e. point of intersection of any two lines lies on the third line It is given that lines 2x + y − 3 = 0 5x + ky − 3 = 0 3x − y − 2 = 0 are concurrent So, finding point of intersection of lines (1) & (3) Adding (1) & (3) (2x + y − 3) + (3x − y − 2) = 0 2x + 3x + y – y − 3 − 2 = 0 5x + 0 − 5 = 0 5x = 5 x = 5/5 x = 1 Putting x = 1 in (1) 2x + y − 3 = 0 2(1) + y − 3 = 0 2 + y − 3 = 0 y − 1 = 0 y = 1 Hence point of intersection of line(1) & (3) is (1, 1) Since lines (1), (2) & (3) are concurrent (1, 1) will satisfy equation of line (2) Putting x = 1 & y = 1 in (2) 5x + ky − 3 = 0 5(1) + k(1) − 3 = 0 5 + k − 3 = 0 k + 5 − 3 = 0 k + 2 = 0 k = −2 Thus, k = −2
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