If a straight line drawn through the point of intersection of the lines $4 x+3 y-1=0$ and $3 x+4 y-1=0$, meets the co-ordinate axes at the points P and Q , then the locus of the mid point of $P Q$ is :
Select the correct option:
A
x+y-7=0
B
x+y-14 x y=0
C
2 x+y+14 x y=0
D
x+2 y-14 x y=0
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution
\begin{aligned}
&\text { Point of intersection of the lines }\\
&3 x+4 y=1 \text { and } 4 x+3 y=1 \text { is }\left(\frac{1}{7}, \frac{1}{7}\right)
\end{aligned} Let the line be $\frac{x}{2 h}+\frac{y}{2 k}=1$ Satisfy $\left(\frac{1}{7}, \frac{1}{7}\right)$
$$
\begin{aligned}
& \frac{1}{14 \mathrm{~h}}+\frac{1}{14 \mathrm{k}}=1 \\
& \frac{1}{\mathrm{x}}+\frac{1}{\mathrm{y}}=14
\end{aligned}
$$
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