Let the line L intersect X-axis at a point (h,0). Slope of line L(m1)=‌
0+3
h−5
=‌
3
h−5
Slope of line (m2),√3x+y−9=0 is −√3 tan‌60∘=|‌
‌
3
h−5
+√3
1−‌
3√3
h−5
|
⇒‌‌√3=|‌
3+√3(h−5)
h−5−3√3
|⇒√3=±‌
3+√3(h−5)
h−5−3√3
When √3=‌
3+√3(h−5)
h−5−3√3
⇒‌‌√3h−5√3−9=3+√3h−5√3 (Not possible) When √3=‌
−(3+√3(h−5))
h−5−3√3
‌⇒‌‌√3h−5√3−9=−3−√3h+5√3 ‌⇒‌‌2√3h=10√3+6⇒h=5+√3 The line L intersect X-axis at point (5+√3,0). Equation of line L is