Mathematics - Circle Question with Solution | TestHub
MathematicsCircleGeneral, Basic geometries, Definition Diametrical form of circleMedium2 minQB
MathematicsMediumsingle choice
Passage / Comprehension
A=(0,0), B=(4,0). P varies with PA=K·PB (K>0, K≠1). Its locus is a circle S meeting AB at D,E. In the companion question, a circle centred at (3,2) touches AB at D=(3,0), hence K=3.
A=(0,0), B=(4,0). P varies with PA=K·PB, where K=3 (as determined by the companion question: the circle centred at (3,2) touches AB at D=(3,0)). Its locus is circle S meeting AB at D,E. If θ is an angle between the tangents from (2,0) to S, find tan θ.
Options:
Answer:
D
Solution:
The companion Q87 gives K=3. Circle S has diameter from (3,0) to (6,0), center (9/2,0), and radius 3/2. From (2,0), tan(θ/2)=3/4; hence tan θ=24/7, option D.
Stream:JEESubject:MathematicsTopic:CircleSubtopic:General, Basic geometries, Definition Diametrical form of circle
⏱ 2mℹ️ Source: QB
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