Pair Of Straight Lines Question 60
Question: 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 $
Show Answer
Answer:
Correct Answer: D
Solution:
Given two lines are $ x-6y=0 $ and $ x-y=0 $ . We know $ \frac{0+x_1+x_2}{3}=1 $
$ \Rightarrow x_1+x_2=3 $ …..(i)
and $ y_1+y_2=0 $ …..(ii)
Also $ x_1-6y_1=0 $ …..(iii)
$ x_2-y_2=0 $ …..(iv)
[Since the point (x1,y1) and $ (x_2,y_2) $ lies on the lines AB and AC respectively]
Now on solving, the coordinates of B and C are $ ( \frac{18}{5},\frac{3}{5} ) $ and $ ( \frac{-3}{5},\frac{-3}{5} ) $ respectively.
Hence the equation of third side i.e., BC is $ 2x-7y-3=0 $ .
BETA
