Mathematics - Circle Question with Solution | TestHub

MathematicsCircleTangent & NormalMedium2 minQB

MathematicsMediumsingle choice

Passage / Comprehension

A circle C of radius 1 touches the x-axis at A, with centre Q in the first quadrant. A tangent from O=(0,0) touches C at T. A point P on OT makes triangle OAP right-angled at A and its perimeter is 8.

A radius-1 circle $C$ touches the $x$ -axis at $A$ , with centre $Q$ in the first quadrant. A tangent from $O = (0, 0)$ touches it at $T$ . A point $P$ on this tangent makes $△ O A P$ right-angled at $A$ with perimeter 8. Find the equation of $C$ .

Options:

Answer:

Solution:

The geometry gives OA=2 and QA=1, so the circle has center Q=(2,1) and radius 1. Its equation is (x-2)²+(y-1)²=1, the repaired option A.

Stream:JEESubject:MathematicsTopic:CircleSubtopic:Tangent & Normal

⏱ 2mℹ️ Source: QB

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