2 lines passing through the point (2,3) intersects each other at an angle of 60 degrees. If slope of one line is 2, find the equation of the other line.

Asked by s_patne2002 | 21st Nov, 2015, 04:38: PM

Expert Answer:

L e t space t h e space s l o p e space o f space t h e space o t h e r space l i n e space b e space apostrophe m apostrophe. S i n c e space t h e space t w o space l i n e s space i n t e r s e c t space a t space 60 space d e g r e e comma tan 60 to the power of o equals open vertical bar fraction numerator m minus 2 over denominator 1 plus 2 m end fraction close vertical bar rightwards double arrow square root of 3 equals plus-or-minus fraction numerator m minus 2 over denominator 1 plus 2 m end fraction rightwards double arrow square root of 3 open parentheses 1 plus 2 m close parentheses equals plus-or-minus open parentheses m minus 2 close parentheses rightwards double arrow m equals fraction numerator negative 2 minus square root of 3 over denominator 2 square root of 3 minus 1 end fraction space o r space m equals fraction numerator 2 minus square root of 3 over denominator 1 plus 2 square root of 3 end fraction S i n c e comma space t h e space s e c o n d space l i n e space a l s o space p a s s e s space t h r o u g h space t h e space p o i n t space left parenthesis 2 comma 3 right parenthesis comma i t s space e q u a t i o n space i n space p o i n t minus s l o p e space f o r m space i s space y minus 3 equals fraction numerator negative 2 minus square root of 3 over denominator 2 square root of 3 minus 1 end fraction open parentheses x minus 2 close parentheses o r y minus 3 equals fraction numerator 2 minus square root of 3 over denominator 1 plus 2 square root of 3 end fraction open parentheses x minus 2 close parentheses

Answered by satyajit samal | 23rd Nov, 2015, 10:36: AM