Let `a x+b y+c=0`
be a variable straight line, where `a , ba n dc`
are the 1st, 3rd, and 7th terms of an increasing AP, respectively.
Then prove that the variable straight line always passes through a fixed
point. Find that point.
Text Solution
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Let the common difference of A.P.be d. Then b=a+2d and c=a+6d. So, given variable straight line will be ax+(a+2d)y+a+6d=0 or a(x+y+1) + d(2y+6)=0 This is the equation of family of straight lines concurrent at point of intersection of lines x+y+1=0 and 2y+6=0 which (2,-3).
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