If 4a+5b+6c=0 then the set of lines ax+by+c=0 are concurrent at the point Options: A . &nbsp(23,56) B . &nbsp(13,12) C . &nbsp(12,43) D . &nbsp(13,73)

If 4a+5b+6c=0 then the set of lines ax+by+c=0 are concurrent at the point

Question

If 4a+5b+6c=0 then the set of lines ax+by+c=0 are concurrent at the point

Options:

A . (23,56)

B . (13,12)

C . (12,43)

D . (13,73)

Answer: Option A
:
A
4a+5b+6c=0
(6x)a+(6y)b+6c=0

\to

[Multiply given set of lines ax+by+c=0 with '6']
Now on comparing 6x=4 and 6y =5
⇒ (x,y) =

(\frac{2}{3}, \frac{5}{6})

∴

ax+by+c=0 must passes through

(\frac{2}{3}, \frac{5}{6})

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