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The set of lines ax+by+c=0, where 3a+2b+...

The set of lines `ax+by+c=0`, where `3a+2b+4c=0` is concurrent at the point…

Text Solution

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The set of lines `ax+by+c=0`, where `3a+2b+4c=0` or `(3)/(4)a+(1)/(2)b+c=0` are concurrent at `(x=(3)/(4),y=(1)/(2))` i.e. comparing the coefficient of `x` and `y`.
Thus, point of concurrency is `((3)/(4),(1)/(2))`
Alternate Solutions
As, `ax+by+c=0`, satisfy `3a+2b+4c=0` which represents system of concurrent lines whose point of concurrency could be obtained by comparison as,
`ax+by+c=(3a)/(4)+(2)/(b)b+c`
`impliesx=(3)/(4)`, `y=(1)/(2)` is point of concurrency.
`:. ((3)/(4),(1)/(2))` is the required point.
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