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A circle always passes through the fixed points (a, 0) and (–a, 0).
Q.
How many tangents can be drawn from the origin to the circle that we get in above question?
- a)0
- b)1
- c)2
- d)3
Correct answer is option 'A'. Can you explain this answer?
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A circle always passes through the fixed points (a, 0) and (a, 0).Q.Ho...
Solution:
Given, the circle always passes through the fixed points (a, 0) and (a, 0).
To find the number of tangents that can be drawn from the origin to this circle, we need to consider two cases:
Case 1: The origin lies outside the circle
In this case, no tangents can be drawn from the origin to the circle. This is because any line passing through the origin will intersect the circle at two distinct points and not just touch it at one point, which is the definition of a tangent.
Case 2: The origin lies inside the circle
In this case, again no tangents can be drawn from the origin to the circle. This is because any line passing through the origin and intersecting the circle will intersect it at two distinct points and not just touch it at one point.
Therefore, the answer is option 'A', i.e., 0 tangents can be drawn from the origin to the circle.
Given, the circle always passes through the fixed points (a, 0) and (a, 0).
To find the number of tangents that can be drawn from the origin to this circle, we need to consider two cases:
Case 1: The origin lies outside the circle
In this case, no tangents can be drawn from the origin to the circle. This is because any line passing through the origin will intersect the circle at two distinct points and not just touch it at one point, which is the definition of a tangent.
Case 2: The origin lies inside the circle
In this case, again no tangents can be drawn from the origin to the circle. This is because any line passing through the origin and intersecting the circle will intersect it at two distinct points and not just touch it at one point.
Therefore, the answer is option 'A', i.e., 0 tangents can be drawn from the origin to the circle.
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