Questions
If a, b, c are three terms of an A.P., then the line ax + by + c = 0
a
has a fixed direction
b
always passes through a fixed point
c
always cuts intercepts on the axes such that their sum is zero
d
forms a triangle with the axes whose area is constant.
detailed solution
Correct option is B
Let a, b, c be pth, qth and rth terms of an A.P. whose first term is A and common difference is d. The given line is ax + by + c = 0⇒[A + (p – 1) d] x + [A + (q – 1) d] y + [A + (r – 1) d] = 0⇒A(x + y + 1) + d((p – 1) x + (q – 1) y + r – 1) = 0⇒The given line passes through the point of intersection of lines x + y + 1 = 0 and ( p – 1) x + (q – 1)y + r – 1 = 0, which is a fixed point.Talk to our academic expert!
Similar Questions
If the lines ax+by+c = 0, bx+cy+a = 0 and cx+ay+b=0 are concurrent then the point of concurrency is
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