SATHEE: Straight Line and Pair of Straight Lines 1 Question 48

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.

$\begin{aligned} \Rightarrow & a_{1} a_{2} & = b_{1} b_{2} \\ or & a_{1} b_{2} + b_{1} a_{2} & = 0 \end{aligned}$

Given lines are, $2 x + 3 y + 19 = 0$

$and 9 x + 6 y - 17 = 0$

Here, $a_{1} = 2, b_{1} = 3, c_{1} = 19$

and $a_{2} = 9, b_{2} = 6, c_{2} = - 17$

$∴ a_{1} a_{2} = 18$

and $b_{1} b_{2} = 18$

$\Rightarrow a_{1} a_{2} = b_{1} b_{2}$ . Thus, points are concyclic.

Hence, given statement is true.

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Straight Line and Pair of Straight Lines 1 Question 48

48. The lines 2x+3y+19=0 and 9x+6y−17=0 cut the coordinate axes in concyclic points.

Solution:

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48. The lines $2 x + 3 y + 19 = 0$ and $9 x + 6 y - 17 = 0$ cut the coordinate axes in concyclic points.