If two sides of a triangle are represented by `x^2_7xy+6y^2=0` and the centroid is `(1,0)` then the equation of third side is

Options

A. `2x+7y+3=0`
B. `2x-7y+3=0`
C. `2x+7y-3=0`
D. `2x-7y-3=0`

Answer

D

Explanation

Given , two lines are `x-6y=0 and x-y=0`.
We know that , `(0+x_1+x_2)/(3)=1`

and `(0+y_1+y_2)/(3)=0`
`rArr x_1+x_2=3 and y_1,y_2=0` ......(i)
Also , `x_1-6y_1=0` ......(ii)
and `x_2-y_2=0` ......(iii)
On solving , coordinates of B and C are `((18)/(5),(3)/(5))` and `((-3)/(5),(-3)/(5))` , respectively.
Hence , the equation of third side i.e., BC is `2x-7y-3=0`.