If ( a , ,, , ,1 a ) , ( b , ,, , ,1 b ) , ( c , ,, , ,1 c ) & ( … - Vidyadip

MCQ

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

A
$4$
B
$1/4$
✓
$1$
D
$16$

✓

Answer

Correct option: C.

$1$

c
Let us assume that circle $: x^2 + y^2 = 16$

points are of form $\left( {t,\;\frac{1}{t}} \right)$

$\Rightarrow t^2 + \frac{1}{{{t^2}}} = 16$ should satisfy

$\Rightarrow t^4 - 16t^2 + 1 = 0 $

$\therefore$ product of roots $= 1 $

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