Check sibling questions

Example 20 - If lines 2x + y - 3 = 0, 5x + ky - 3 = 0 concurrent

Example 20 - Chapter 10 Class 11 Straight Lines - Part 2
Example 20 - Chapter 10 Class 11 Straight Lines - Part 3

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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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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.