Q69.The locus of the centres of the circles, which touch the circle, ๐ฅ2 + ๐ฆ2 = 1 externally, also touch the ๐ฆ-axis and lie in the first quadrant, is: (1) ๐ฆ= โ1 + 2๐ฅ, ๐ฅโฅ0 (2) ๐ฆ= โ1 + 4๐ฅ, ๐ฅโฅ0 (3) ๐ฅ= โ1 + 2๐ฆ, ๐ฆโฅ0 (4) ๐ฅ= โ1 + 4๐ฆ, ๐ฆโฅ0
What This Question Tests
This problem involves finding the locus of the center of a circle satisfying multiple geometric conditions: external tangency to another circle and tangency to the y-axis, requiring careful application of distance formulas.
Concepts Tested
Formulas Used
Distance between centers = sum of radii for external touch
Distance from y-axis = x-coordinate of center
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๐ Question Details
- Chapter
- Circles
- Topic
- Locus of center of circles
- Year
- 2019
- Shift
- 10 Apr Shift 2
- Q Number
- Q69
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections (briefly touched in Circles for locus)
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