Q71.The area (in sq. units) of the smaller of the two circles that touch the parabola, y2 = 4x at the point (1, 2) and the x -axis is (1) 8π(3 −2√2) (2) 8π(2 −√2) + (3) 4π(3 √2) (4) 4π(2 −√2)
What This Question Tests
This is a multi-concept problem requiring the equation of the tangent to a parabola at a given point, and then using the properties of a circle that touches this tangent and the x-axis. This leads to finding the center and radius of the circle and subsequently its area.
Concepts Tested
Formulas Used
Tangent to y^2=4ax at (x1,y1): yy1 = 2a(x+x1)
Circle touching x-axis: C=(h,r), radius=r
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📋 Question Details
- Chapter
- Applications of Derivatives
- Topic
- Tangent to parabola and circle properties
- Year
- 2019
- Shift
- 09 Apr Shift 2
- Q Number
- Q71
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 6: Applications of Derivatives
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