If a,b,c are any three terms of an AP then the line ax+by+c=0

JEE Advanced Mathematics question

If are any three terms of an AP then the line

(A)has a fixed direction
(B)always passes through a fixed pointCorrect
(C)always cuts intercepts on the axes such that their sum is zero
(D)forms a triangle with the axes whose area is constant

Answer: (B)

Solution

For consecutive terms, , i.e. the point satisfies for every such : a fixed point. More generally (book's approach), if are the th, th, th terms of an AP with first term and common difference , the line is

λ(x+y+1)+

See the full step-by-step solution

Create a free account to read the complete working (3 steps), and practise questions like this in a timed test.

Create a free account

Question ID VK-108803