Find the conditions that the straight lines `y=m_1x+c_1, y=m_2x+c_2a n d\ y=m_2x+c_3` may meet in a point.

Explanation

It is given that the three lines are concurrent.


so,`|[m_1,-1,c_1],[m_2,-1,c_2],[m_3,-1,c_3]|`


`⇒ m1(-c3 + c2) + 1(m2c3-m3c2) + c1(-m2 + m3) = 0 `

`
⇒ m1(c2-c3) + m2(c3-c1) + m3(c1-c2) = 0 `

Hence, the required condition is `m1(c2-c3) + m2(c3-c1) + m3(c1-c2) = 0`