Points A(α,−3),B(2,0) and C(1,α) are collinear.
∴ Slope of AB= Slope of BC ⇒‌
0+3
2−α
=‌
α−0
1−2
⇒−3=α(2−α) ⇒−3=2α−α2 ⇒α2−2α−3=0 ⇒α2−3α+α−3=0 ⇒α(α−3)+1(α−3)=0 ⇒(α+1)(α−3)=0⇒α=−1,3 Given, α1<α2 ∴α1=1‌ and ‌α2=3 ∴(α1,α2)=(−1,3) Now, equation of the line passing through (−1,3) and making angle ‌
Ï€
3
with positive x-axis is (y−y1)=m(x−x1) ⇒y−3=(tan‌