Question
Question: If a<sup>2</sup> + b<sup>2</sup> – c<sup>2</sup> – 2ab = 0, then the family of straight lines ax + b...
If a2 + b2 – c2 – 2ab = 0, then the family of straight lines ax + by + c = 0 is concurrent at the points-
A
(–1, 1), (1, – 1)
B
(1, 1), (1, – 1)
C
(–1, –1), (1, 1)
D
(–1, –1)
Answer
(–1, 1), (1, – 1)
Explanation
Solution
Given, a2 + b2 – c2 – 2ab = 0
Ž (a – b)2 – c2 = 0
Ž (a – b – c) (a – b + c) = 0
Ž – a + b + c = 0 or a – b + c = 0
On comparing with ax + by + c = 0.
The points of concurrency are (–1, 1) or (1, – 1)