Q84.Let P(α, β) be a point on the parabola y2 = 4x. If P also lies on the chord of the parabola x2 = 8y whose mid point is (1, 54 ), then (α −28)(β −8) is equal to _______.
What This Question Tests
The question combines properties of two different parabolas and the concept of a chord with a given midpoint. It tests the ability to apply standard formulas for conic sections and simultaneous equations.
Concepts Tested
Formulas Used
y^2 = 4ax
x^2 = 4by
T = S1 (for chord with given midpoint)
📚 NCERT Sections This Tests
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📋 Question Details
- Chapter
- Coordinate Geometry
- Topic
- Parabola, Chord of a parabola, Midpoint of a chord
- Year
- 2024
- Shift
- 29 Jan Shift 2
- Q Number
- Q84
- Type
- Numerical
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections
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