Question

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 $=$

• A. 4
• B. $1 / 4$
• C. 1
• D. 16

Answer 1

Answer: (C)

Let equation of the circle be
$x^2+y^2+2 g x+2 f y+\lambda=0$
$\left(t, \frac{1}{t}\right)$ be a point on the circle
$\therefore t ^2+\frac{1}{ t ^2}+2 gt +2 f \frac{1}{ t }+\lambda=0 $
$ t ^4+2 gt ^3+\lambda t ^2+2 ft +1=0$
roots of the above equation are $a , b , c ,\, \&\, d$
$\therefore abcd =1$