Question

find the condition that the line 4x + 5y = 0 coincide with one of the lines given by ax square + 2hxy + by square = 0

Answer 1

Step-by-step explanation:

Given Find the condition that the line 4x + 5y = 0 coincide with one of the lines given by ax square + 2hxy + by square = 0

• We know that auxiliary equation is given by bm^2 + 2hm + a = 0
• Given ax^2 + 2hxy + by^2 = 0
• So ax + 2h(y/x) + b(y/x)^2 = 0
• Now line is 4x + 5y = 0
• Or 5y = - 4x
• Or y/x = - 4 / 5  is the slope.
• So a + 2h(- 4/5) + b(- 4/5)^2 = 0
• So a - 8h/5 + 16b/25 = 0
• Or 25 a - 40 h + 16 b = 0