If 16a2 + 25b2- c2 = 40ab, then the family of lines ax + by + c = 0 is concurrent at the points)
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(4 , - 5) & (-4 , 5) are the points at which family of lines ax + by + c = 0 is concurrent
Step-by-step explanation:
16a² + 25b² - c² = 40ab
=> (4a)² + (5b)² - 40ab = c²
=> (4a)² + (5b)² - 2(4a)(5b) = c²
=> (4a - 5b)² = c²
=> 4a - 5b = c or - c
=> 4a - 5b + c = 0
comparing with ax + by + c = 0
=> x = 4 , y = -5
4a - 5b - c = 0
=> -4a + 5b + c = 0
comparing with ax + by + c = 0
=> x = -4 , y = 5
(4 , - 5) & (-4 , 5) are the points at which family of lines ax + by + c = 0 is concurrent
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