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प्रश्न
Find the condition that the line 3x + y = 0 may be perpendicular to one of the lines given by ax2 + 2hxy + by2 = 0
उत्तर
The auxiliary equation of the lines represented by ax2 + 2hxy + by2 = 0 is bm2 + 2hm + a = 0
Since one line is perpendicular to the line 3x + y = 0 whose slope is `- 3/1 = - 3`
∴ slope of that line = m = `1/3`
∴ m = `1/3` is the root of the auxiliary equation bm2 + 2hm + a = 0.
∴ `"b"(1/3)^2 + "2h"(1/3) + "a" = 0`
∴ `"b"/9 + "2h"/3 + "a" = 0`
∴ b + 6h + 9a = 0
∴ 9a + b + 6h = 0
This is the required condition.
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