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

$[\frac{2 a b^{2}}{a^{2} + b^{2}}, \frac{2 a^{2} b}{a^{2} + b^{2}}]$

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$[\frac{2 a^{2} b}{a^{2} + b^{2}}, \frac{2 a b^{2}}{a^{2} + b^{2}}]$

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$[\frac{2 a b}{a^{2} + b^{2}}, \frac{2 a b}{a^{2} + b^{2}}]$

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$(a, b)$

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Solution

The correct option is A
$[\frac{2 a b^{2}}{a^{2} + b^{2}}, \frac{2 a^{2} b}{a^{2} + b^{2}}]$

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.
$∴ \frac{h}{a} + \frac{k}{b} = 2$
$- \frac{b}{a} \times \frac{k}{h} = - 1$
$\Rightarrow h = \frac{2 a b^{2}}{a^{2} + b^{2}} k = \frac{2 a^{2} b}{a^{2} + b^{2}}$

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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

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