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The number of common tangents to the circles and is
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. (c)
Central Idea Number of common tangents depend on the position of the circle with respect to each other.
(i) If circles touch externally common tangents
(ii) If circles touch internally common tangent
(iii) If circles do not touch each other, 4 common tangents
Given equations of circles are
.....(i) and
.....(ii)
Centre of circle (i) is and radius
Centre of circle (ii) is and radius
, (say)
Now,
Thus, both circles touch each other externally.
Hence, there are three common tangents.
Central Idea Number of common tangents depend on the position of the circle with respect to each other.
(i) If circles touch externally common tangents
(ii) If circles touch internally common tangent
(iii) If circles do not touch each other, 4 common tangents
Given equations of circles are
.....(i) and
.....(ii)
Centre of circle (i) is and radius
Centre of circle (ii) is and radius
, (say)
Now,
Thus, both circles touch each other externally.
Hence, there are three common tangents.
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Question Text | The number of common tangents to the circles and is |
Updated On | Sep 29, 2023 |
Topic | Conic Sections |
Subject | Mathematics |
Class | Class 11 |
Answer Type | Text solution:1 Video solution: 3 |
Upvotes | 411 |
Avg. Video Duration | 8 min |