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

True

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False

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Solution

The correct option is A True
Two lines at the coordinates axis in concylic points when $a \times d = b \times c$
Now $2 x + 3 y + 19 = 0$ And $9 x + 6 y - 17 = 0$
$\Rightarrow \frac{x}{\frac{- 19}{2}} + \frac{y}{\frac{- 9}{3}} \frac{x}{\frac{17}{9}} + \frac{y}{\frac{17}{6}} = 1$
$∴ \frac{- 19}{2} \times \frac{17}{9} = \frac{- 19}{3} \times \frac{17}{6} (p r o v e d)$

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

The correct option is A TrueTwo lines at the coordinates axis in concylic points when a×d=b×cNow 2x+3y+19=0 And 9x+6y−17=0⇒x−192+y−93x179+y176=1∴−192×179=−193×176(proved)

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