Q65.Let the tangent drawn to the parabola y2 = 24x at the point (α, β) is perpendicular to the line 2x + 2y = 5 . Then the normal to the hyperbola x2 −y2 = 1 at the point (α + 4, β + 4) does NOT pass through the point: α2 β2 (1) (25, 10) (2) (20, 12) (3) (30, 8) (4) (15, 13)
What This Question Tests
This question integrates concepts of tangents to parabolas and normals to hyperbolas, requiring calculation of slopes, point coordinates, and verifying point membership on a line.
Concepts Tested
Formulas Used
Tangent to y²=4ax at (x₁,y₁): yy₁ = 2a(x+x₁)
Slope of line ax+by=c is -a/b
Condition for perpendicular lines: m₁m₂ = -1
Normal to x²/a² - y²/b² = 1 at (x₁,y₁): a²x/x₁ + b²y/y₁ = a²+b²
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📋 Question Details
- Chapter
- Coordinate Geometry
- Topic
- Tangent and Normal to Conics
- Year
- 2022
- Shift
- 26 Jul Shift 1
- Q Number
- Q65
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections
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