Example 20 - Chapter 10 Class 11 Straight Lines (Term 1)
Last updated at Feb. 3, 2020 by Teachoo
Examples
Example 1 (a)
Example 1 (b)
Example 1 (c) Important
Example 1 (d)
Example 2 Important
Example 3 Important
Example 4
Example 5
Example 6 Important
Example 7
Example 8
Example 9 (i)
Example 9 (ii) Important
Example 10
Example 11
Example 12
Example 13 Important
Example 14 Important
Example 15 Important
Example 16
Example 17
Example 18 Important
Example 19
Example 20 You are here
Example 21 Important
Example 22 Important
Example 23
Example 24 Important
Example 25 Important
Chapter 10 Class 11 Straight Lines (Term 1)
Serial order wise
- Ex 10.1
- Ex 10.2
- Ex 10.3
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Examples
- Miscellaneous
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
