Straight Line and Pair of Straight Lines 1 Question 48
48. The lines $2 x+3 y+19=0$ and $9 x+6 y-17=0$ cut the coordinate axes in concyclic points.
(1988, 1M)
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Solution:
- Since, $a _1 x+b _1 y+c _1=0$ and $a _2 x+b _2 y+c _2=0$ cuts the coordinate axes at concyclic points.
$$ \begin{array}{rlrl} \Rightarrow & a _1 a _2 & =b _1 b _2 \\ \text { or } & & a _1 b _2+b _1 a _2 & =0 \end{array} $$
Given lines are, $2 x+3 y+19=0$
$$ \text { and } \quad 9 x+6 y-17=0 $$
Here, $\quad a _1=2, b _1=3, c _1=19$
and $\quad a _2=9, b _2=6, c _2=-17$
$\therefore \quad a _1 a _2=18$
and $\quad b _1 b _2=18$
$\Rightarrow a _1 a _2=b _1 b _2$. Thus, points are concyclic.
Hence, given statement is true.
