Expressions in the sum and product of the slopes of a homogeneous pair
This type of question, asked 4 times: 9 May 2024 S2, 19 Apr 2026 S2, 20 Apr 2026 S2, 14 May 2026 S2. All 4 questions below, oldest first.
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Question 1
9 May 2024 S2
101If the slope of one of the lines represented by ax2+(2a+1)xy+2y2=0 is reciprocal of the slope of the other, then the sum of squares of slopes is
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Question 2
19 Apr 2026 S2
55If two lines represented by x2−(1+3)xy+3y2=0 make angles α and β with the X-axis, then tan(α+β) is...
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Question 3
20 Apr 2026 S2
56If the angle made by the lines represented by the equation ax2+2hxy+by2=0 with X-axis are α and β, then tan(α+β) is
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Question 4
14 May 2026 S2
60If the sum of the cubes of slopes of two lines represented by the equation ax2+2hxy+by2=0 is 1, then
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