If $\left( a,\frac{1}{a} \right),\left( b,\frac{1}{b} \right),\left( c,\frac{1}{c} \right)$ and $\le

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If $\left( a,\frac{1}{a} \right),\left( b,\frac{1}{b} \right),\left( c,\frac{1}{c} \right)$ and $\left( d,\frac{1}{d} \right)$ are four distinct points on a circle of radius 4 units then, $abcd$ is equal to:

Accepted Answer

[Key Concept: Four points $(t,\frac{1}{t})$ on a circle of radius $4$: the product of the parameters is $1$.]Let circle is$$x^{2} + y^{2} + 2gx + 2fy + c = 0$$$$\left( d,\frac{1}{d} \right)*\left( a,\frac{1}{b} \right)*\left( a,\frac{1}{a} \right)$$$$Put\left( t,\frac{1}{t} \right)$$$$\Rightarrow \ abcd = 1 $$

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