Question

If a, b, c are in A.P. then ax + by + c = 0 represents 

(a) a single line

(b) a family of concurrent lines

(c) a family of parallel lines

(d) a family of circle   

Answer 1

The correct option (b) a family of concurrent lines

Explanation:

a, b, c are in A.P. hence a + c = 2b.

i.e. a – 2b + c = 0

∴ for x = 1 and y = – 2, ax + by + c = 0 is a line passing through (1, – 2)

∴ ax + by + c = 0 is a family of concurrent lines.