Q64.If ๐ฆ= ๐1๐ฅ+ ๐1 and ๐ฆ= ๐2๐ฅ+ ๐2, ๐1 โ ๐2 are two common tangents of circle ๐ฅ2 + ๐ฆ2 = 2 and parabola ๐ฆ2 = ๐ฅ, then the value of 8 ๐1 ๐2 is equal to (1) 3โ2 - 4 (2) 6โ2 - 4 (3) -5 + 6โ2 (4) 3 + 4โ2
What This Question Tests
This question requires finding the common tangents to a given circle and a parabola by applying their respective conditions for tangency and solving for the slopes.
Concepts Tested
Formulas Used
Equation of tangent to y^2=4ax is y=mx+a/m
Distance from center (0,0) to y=mx+c is |c|/sqrt(m^2+1) = r
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๐ Question Details
- Chapter
- Parabola
- Topic
- Common tangents to circle and parabola
- Year
- 2022
- Shift
- 25 Jun Shift 1
- Q Number
- Q64
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections
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