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प्रश्न
The slope of one of the straight lines ax2 + 2hxy + by2 = 0 is three times the other, show that 3h2 = 4ab
उत्तर
The equation of the given straight line is
ax2 + 2hxy + by2 = 0 .......(1)
Given that the slopes of the lines are m and 3m.
∴ m + 3m = `- (2"h")/"b"`
(m)(3m) = `"a"/"b"`
4m = `- (2"h")/"b"`
and
3m2 = `"a"/"b"`
m = `- "h"/(2"b")`
⇒ `3(- "h"/(2"b"))^3 = "a"/"b"`
⇒ `3 "h"^2/(4"b"^2) = "a"/"b"`
⇒ 3h2 = 4ab
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