Q66.If the orthocentre of the triangle, whose vertices are 1, 2, 2, 3 and 3, 1 is ๐ผ, ๐ฝ, then the quadratic equation whose roots are ๐ผ+ 4๐ฝ and 4๐ผ+ ๐ฝ, is (1) ๐ฅ2 - 19๐ฅ+ 90 = 0 (2) ๐ฅ2 - 18๐ฅ+ 80 = 0 (3) ๐ฅ2 - 22๐ฅ+ 120 = 0 (4) ๐ฅ2 - 20๐ฅ+ 99 = 0
What This Question Tests
This question combines coordinate geometry concepts to find the orthocentre of a triangle and then uses algebra to form a quadratic equation from expressions involving its coordinates.
Concepts Tested
Formulas Used
Slope of perpendicular lines m1m2 = -1
Equation of line y - y1 = m(x - x1)
Sum and product of roots for quadratic equation
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๐ Question Details
- Chapter
- Coordinate Geometry
- Topic
- Orthocentre of a triangle
- Year
- 2023
- Shift
- 01 Feb Shift 1
- Q Number
- Q66
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 10: Straight Lines
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