Circles
The length of tangent from point (5, 4) to circle x² + y² = 9 is
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About This Question
- Subject
- mathematics
- Chapter
- coordinate geometry
- Topic
- circles
- Difficulty
- Hard
- Year
- 2025
Solution
Correct Answer:
√32
- Formula: The length of a tangent L from an external point (x1,y1) to circle x2+y2−r2=0 is L=x12+y12−r2.
- Identify Data: Point is (5,4), Circle is x2+y2−9=0 (r2=9).
- Calculate Power of Point:
- S1=52+42−9=25+16−9=32.
- Extract Length:
- L=32=42.
This hard difficulty mathematics question is from the chapter coordinate geometry, covering the topic of circles. It appeared in the 2025 exam.
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