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Question
The slope of one of the straight lines ax2 + 2hxy + by2 = 0 is twice that of the other, show that 8h2 = 9ab
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Solution
The equation of the given straight line is
ax2 + 2hxy + by2 = 0 .......(1)
Given that the slopes of the straight lines are m and 2m
∴ m + 2m = `- (2"h")/"b"`
(m)(2m) = `"a"/"b"`
3 m = `- (2"h")/"b"`
and
2m2 = `"a"/"b"`
m = `- (2"h")/(3"b")`
⇒ `2( - (2"h")/(3"b"))^2 = "a"/"b"`
⇒ `2((4"h"^2)/(9"b"^2)) = "a"/"b"`
⇒ 8h2 = 9ab
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