Q65.Let C be a circle with radius √10 units and centre at the origin. Let the line x + y = 2 intersects the circle C at the points P and Q. Let MN be a chord of C of length 2 unit and slope -1. Then, a distance (in units) between the chord PQ and the chord MN is (1) 3 −√2 (2) √2 + 1 (3) √2 −1 (4) 2 −√3
What This Question Tests
This question requires finding the equation of two chords and then calculating the distance between them. It involves using properties of circles, lines, and the condition for perpendicularity (for slope -1 and radius perpendicular to chord).
Concepts Tested
Formulas Used
Equation of chord T = S1
Distance from origin to line ax+by+c=0 is |c|/√(a²+b²)
Length of chord = 2√(r² - d²)
Equation of line given point and slope
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📋 Question Details
- Chapter
- Circles
- Topic
- Chords of a circle
- Year
- 2024
- Shift
- 04 Apr Shift 2
- Q Number
- Q65
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections (briefly), Class 12 Mathematics Ch 10: Vectors (Dot product for perpendicularity might be used for slope -1)
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