What is the number of tangents that can be drawn from (1, 2) to the circle x² + y² = 5?
Understand the Problem
The question asks us to find out how many tangent lines can be drawn from the point (1,2) to the circle defined by the equation x² + y² = 5. To solve this problem, we first determine if the point (1, 2) lies inside, outside, or on the circle. Then we will use this information to determine the number of tangent lines.
Answer
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Answer for screen readers
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Steps to Solve
- Check if the point is inside, outside, or on the circle
To determine the number of tangent lines that can be drawn from the point (1, 2) to the circle $x^2 + y^2 = 5$, we first need to check the location of the point with respect to the circle. We do this by plugging the coordinates of the point into the equation of the circle: $$(1)^2 + (2)^2 = 1 + 4 = 5$$ Since the result is equal to 5, the point (1, 2) lies on the circle.
- Determine the number of tangent lines
If a point lies on the circle, exactly one tangent line can be drawn at that point.
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More Information
A line tangent to a circle touches the circle at exactly one point. Since (1,2) lies on the circle $x^2 + y^2 = 5$, there is exactly one tangent line at that point.
Tips
A common mistake is to confuse the conditions for drawing tangents from a point inside, outside, or on the circle. If the point were inside the circle, no tangents could be drawn. If the point were outside the circle, two tangents could be drawn.
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