Q67.If the shortest distance of the parabola y2 = 4x from the centre of the circle x2 + y2 −4x −16y + 64 = 0 is d , then d2 is equal to : (1) 16 (2) 24 (3) 20 (4) 36 y2 x2
What This Question Tests
This question requires finding the center of a circle and then calculating the shortest distance from this point to a parabola, which often involves finding the foot of the normal from the point to the parabola.
Concepts Tested
Formulas Used
y² = 4ax
Center of circle: (-g, -f)
Distance formula: √((x2-x1)² + (y2-y1)²)
Normal to y² = 4ax is y = mx - 2am - am³
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📋 Question Details
- Chapter
- Parabola
- Topic
- Shortest distance between a point and a parabola
- Year
- 2024
- Shift
- 27 Jan Shift 1
- Q Number
- Q67
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections
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