Math, asked by polakshwala0nudhave, 1 year ago

Two lines passing through the point (2, 3) intersect each other at an angle of 60 0 . If the slope of one line is 2. Find the equation of the other line.

Answers

Answered by abhi178
27
let m1 and m2 are the slope of two lines
we know ,
tan@=mod {(m1-m2)/(1+m1.m2)}
where @ is angle between two lines
hence,
tan60=mod {(2-m2)/(1+2m2)}
root3mod {(1+2m2)}=mod {2-m2}
root3 (1+2m2)=+_(2-m2)
root3+2root3 m2=+_(2-m2)

hence
m2=(2-root3)/(1+2root3) , (2+root3)/(1-2root3)

now equation of line ,
(y-3)=m2 (x-2)
put m2 value and equation
(1+2root3)(y-3)=(2-root3)(x-2)

or,
(1-2root3)(y-3)=(2+root3)(x-2)
Answered by kvnmurty
17
Two lines are possible.

P(2,3)
Given  L1 :  slope = 2
Let  L2 be :  y = m x + c

case 1)

Tan 60° = (m1 - m2) / [1 + m1 m2]
        √3 = (2 - m) / (1 + 2 m)
      2 - m = √3 + 2√3 m
      m = (2 - √3) / (2√3 + 1) = (2-√3)(2√3 -1) / 11 
       m = (5√3 - 8) / 11

So :    L2 :  y = (5√3 - 8) /11  * x  + c
        P(2,3) lies on it.
                   3 = (5√3 - 8)/11 * 2 + c
                    c = (49 - 10√3) / 11

So ans:   11 y = (5 √3 - 8) x + (49 - 10√3)

case 2:   angle = -60 deg

Tan (-60°) = (m1 - m2) / [1 + m1 m2]
       -√3 = (2 - m) / (1 + 2 m)
      2 - m = -√3 - 2√3 m
      m = - (2 + √3) / (2√3 - 1) = - (2+√3)(2√3+1) / 11 
       m = - (5√3 + 8) / 11

So :    L2 :  y = - (5√3 + 8) /11  * x  + c
        P(2,3) lies on it.
                   3 = - (5√3 + 8)/11 * 2 + c
                    c = (49 + 10√3) / 11

So ans:   11 y = - (5 √3 + 8) x + (49 + 10√3)
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