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Question

A circle passes through the origin O and cuts the axis at A(a, 0) and B(0, b). The reflection of O in the line AB is the point


A

[2ab2a2+b2,2a2ba2+b2]

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B

[2a2ba2+b2,2ab2a2+b2]

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C

[2aba2+b2,2aba2+b2]

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D

(a,b)

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Solution

The correct option is A

[2ab2a2+b2,2a2ba2+b2]


Equation of AB is x/a+y/b=1. If P(h,k) is the reflection of O in AB then (h/2, k/2) lies on AB and AB and OP are at right angles.
ha+kb=2
ba×kh=1
h=2ab2a2+b2k=2a2ba2+b2


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