The-lines-ax-2y-1-0-bx-3y-1-0-and-cx-4y-1-0-are-concurrent-if-a-b-c-are-in-G-P-

Question Number 76245 by vishalbhardwaj last updated on 25/Dec/19

The lines a x + 2 y + 1 = 0, b x + 3 y + 1 = 0

and c x + 4 y + 1 = 0 are concurrent

if a, b, c are in G . P . ? ?

Answered by MJS last updated on 25/Dec/19

no, they are parallel if a = 2 k \land b = 3 k \land c = 4 k

2 k x + 2 y + 1 = 0 \Leftrightarrow k x + y + \frac{1}{2} = 0

3 k x + 3 y + 1 = 0 \Leftrightarrow k x + y + \frac{1}{3} = 0

4 k x + 4 y + 1 = 0 \Leftrightarrow k x + y + \frac{1}{4} = 0

since the constant factors are never the

same the lines are never concurrent

Facebook Tweet Pin