A) \[2x-y=9\]
B) \[({{p}^{2}}+{{q}^{2}}-1)(px+qy-1)=(2p-1)(qx+py-1)\]
C) \[(pq-1)(px+qy-1)=({{p}^{2}}+{{q}^{2}}-1)(qx+py-1)\]
D) None of these
Correct Answer: A
Solution :
Since the median passes through A, the intersection of the given lines. Its equation is given by \[(px+qy-1)+\lambda (qx+py-1)=0\], where \[\lambda \] is some real number. Also, since the median passes through the point (p, q), we have \[({{p}^{2}}+{{q}^{2}}-1)+\lambda (qp+pq-1)=0\] Þ \[\lambda =-\frac{{{p}^{2}}+{{q}^{2}}-1}{2pq-1}\] and the equation of median through A is \[(px+qy-1)-\frac{{{p}^{2}}+{{q}^{2}}-1}{2pq-1}(qx+py-1)=0\] Þ \[(2pq-1)(px+qy-1)=({{p}^{2}}+{{q}^{2}}-1)(qx+py-1)\].
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