Concurrency Of Three Lines And Family Of Straight Lines

Concept And Use of Family of Straight Lines

Concurrent lines

If a^2+b^2-c^2-2ab , then the point of concurrency of family of straight lines ax+by+c=0 lies on line

If a^(2)+4b^(2)-9c^(2)=4ab , then the line on which is meet the point of concurrency of family of straight line ax+by+3c=0 lies is

Condition for concurrency of three lines

If 3a+2b+4c=0 then show that the equation ax+by+c=0 represents a family of concurrent straight lines and find the point of concurrency.

Assertion: Number of triangles formed by n concurrent lines and a line which is parallel to one of the n concurrent lines is "^(n-1)C_2. Reason: One and only one triangle is formed by three lines out of which 2 are concurrent and third line is not passing through the point of intersection of the concurrent lines and not parallel to any of the concurrent lines. (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not the correct explanation of A (C) A is true but R is false. (D) A is false but R is true.