1. Class 11
2. Important Question for exams Class 11
3. Chapter 10 Class 11 Straight Lines

Transcript

Misc 12 Find the equation of the line passing through the point of intersection of the lines 4x + 7y – 3 = 0 and 2x – 3y + 1 = 0 that has equal intercepts on the axes. Given lines are 4x + 7y − 3 = 0 2x – 3y + 1 = 0 We need to calculate Equation of line that passes through point of intersection of lines (1) & (2) & make equal intercepts on the axes Calculating point of intersection of lines (1) & (2) From (2) 2x − 3y + 1 = 0 2x = 3y − 1 x = (3𝑦 − 1)/2 Putting value of x in (1) 4x + 7y − 3 = 0 4((3𝑦 − 1)/2) + 7y − 3 = 0 2(3y − 1) + 7y − 3 = 0 6y − 2 + 7y − 3 = 0 13y − 5 = 0 13y = 5 y = 5/13 Putting value of y = 5/13 in (1) 2x − 3y + 1 = 0 2x − 3(5/13) + 1 = 0 2x − 15/13 + 1 = 0 2x = 15/13 – 1 2x = (15 − 13)/13 2x = 2/13 x = 2/(13 × 2) x = 1/13 Thus, point of intersection is (1/13, 5/13) Given that equation of line makes equal intercepts on the axes Let equation of line be 𝑥/𝑎 + 𝑦/𝑏 = 1 Where a is x − intercept & b is y − intercept Here both intercepts are same, So, b = a So equation of line becomes 𝑥/𝑎 + 𝑦/𝑎 = 1 x + y = a Also the line passes through (1/13, 5/13) Putting x = 1/13, y = 5/13 in our equation x + y = a 1/13 + 5/13 = a 6/13 = a a = 6/13 Thus, the equation of required lines becomes x + y = a x + y = 6/13 13(x + y) = 6 13x + 13y = 6 13x + 13y − 6 = 0

Chapter 10 Class 11 Straight Lines

Class 11
Important Question for exams Class 11