Q67.The locus of the point of intersection of the straight lines, tx −2y −3t = 0 and x −2ty + 3 = 0 (t ∈R), is: (1) A hyperbola with the length of conjugate axis 3 (2) A hyperbola with eccentricity √5 (3) An ellipse with the length of major axis 6 (4) An ellipse with eccentricity 2 √5
What This Question Tests
The problem requires finding the locus of the intersection point of two lines by eliminating the parameter 't' and identifying the resulting equation as a hyperbola.
Concepts Tested
Formulas Used
Equation of a hyperbola x²/a² - y²/b² = 1
Length of conjugate axis 2b
Eccentricity e = √(1 + b²/a²)
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📋 Question Details
- Chapter
- Coordinate Geometry
- Topic
- Locus of a point
- Year
- 2017
- Shift
- 08 Apr Online
- Q Number
- Q67
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections
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