Check sibling questions

Ex 10.3, 11 - Prove that line through (x1, y1) and parallel - Two lines // or/and prependicular

Ex 10.3, 11 - Chapter 10 Class 11 Straight Lines - Part 2
Ex 10.3, 11 - Chapter 10 Class 11 Straight Lines - Part 3

Get Real time Doubt solving from 8pm to 12 am!


Transcript

Ex 10.3, 11 Prove that the line through the point (x1, y1) and parallel to the line Ax + By + C = 0 is A (x – x1) + B (y – y1) = 0. The line passing through (x1, y1) and parallel to the line Ax + By + C = 0 has the same slope as the line Ax + By + C = 0 Finding slope of Ax + By + C = 0 By = − Ax − C y = ( − 𝐴𝑥 − 𝐶)/𝐵 y = (( − 𝐴)/𝐵) x + (( −𝐶)/𝐵) The above equation is of the form y = mx + c Where m = slope of line Slope of line (Ax + By + C = 0) = ( − 𝐴)/𝐵 Since both lines are parallel Slope of the required line also same Hence, Slope of required line = − 𝐴/𝐵 Now, finding equation of line We know that equation of a line passing through the point (x1, y1) & having slope m is (y – y1) = m (x – x1) So, equation of line passing through point (x1, y1) & having slope (−𝐴)/𝐵 is (y – y1) = − 𝐴/𝐵(x – x1) B (y – y1) = − A (x – x1) By − By1 = − Ax + Ax1 Ax − Ax1 + By − By1 = 0 A(x – x1) + B(y – y1) = 0 Which is the required equation Hence proved

Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

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.