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  • The base B C of \triangle A B C is bisected at (p, q) and equation of sides A B and A C are <img alt="p x+q y=1" src="https://entrancecorner.oncodecogs.com/gif.latex?p%20x&plus;q%20y%

The base B C of \triangle A B C is bisected at (p, q) and equation of sides A B and A C are p x+q y=1 and  . Then, equation of median through A is
 

 

Option: 1

(2 p q-1)(p x+q y-1)=\left(p^2+q^2-1\right)(q x+p y-1)


 


Option: 2

(q x+q y-1)(q x+p y-1)=0
 


Option: 3

(p x+q y-1)(q x-p y-1)=0
 


Option: 4

None of the above


Answers (1)

best_answer

Any line through A is given by
(p x+q y-1)+\lambda(q x+p y-1)=0
which is passing through (p, q).
Hence,
\lambda=-\frac{\left(p^2+q^2-1\right)}{(2 p q-1)}
Thus, the required line is
\begin{aligned} & (p x+q y-1)-\frac{\left(p^2+q^2-1\right)}{(2 p q-1)} \cdot(q x+p y-1)=0 \\ \Rightarrow \quad & (2 p q-1)(p x+q y-1)=\left(p^2+q^2-1\right)(q x+p y-1) \end{aligned}

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