Question

If 16a2 + 25b2- c2 = 40ab, then the family of lines ax + by + c = 0 is concurrent at the points)
Thank You.

Answer 1

(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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