1.

Find k, if one of the lines given by 6x2 + kxy + y2 = 0 is 2x + y = 0.

Answer»

Given equation is 6x2 + kxy + y2 = 0. 

Its auxiliary equation is m2 + km + 6 = 0 

Since, 2x + y = 0 is one of the lines given by 6x2 + kxy + y2 = 0 

Slope of the line 2x + y = 0 is -2. 

∴ - 2 is one of the roots of the auxiliary equation m2 + km + 6 = 0 

∴ (- 2)2 + k(-2) + 6 = 0

∴ 4 - 2k + 6 = 0 

∴ 2k = 10 

∴ k = 5



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