Q85.The equations of the sides AB, BC and CA of a triangle ABC are 2x + y = 0, x + py = 15a and x −y = 3 respectively. If its orthocentre is (2, a), −12 < a < 2 , then p is equal to
What This Question Tests
This question tests the ability to find the slopes of lines, apply the condition for perpendicularity for altitudes, and use the orthocentre's coordinates to form and solve equations.
Concepts Tested
Formulas Used
Slope of line ax+by+c=0 is -a/b
Condition for perpendicular lines: m1m2 = -1
Orthocentre is intersection of altitudes
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📋 Question Details
- Chapter
- Straight Lines
- Topic
- Orthocentre of a triangle
- Year
- 2022
- Shift
- 26 Jul Shift 1
- Q Number
- Q85
- Type
- Numerical
- NCERT Ref
- Class 11 Mathematics Ch 10: Straight Lines
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