Question

If $(a,\frac{1}{a}),(b,\frac{1}{b}),(c,\frac{1}{c})$ and $(d,\frac{1}{d})$ are four distinct points on a circle of radius $4$ units then, $abcd=$

• A. $4$
• B. $\frac{1}{4}$
• C. $1$
• D. $16$

Answer 1

Answer: (C)

$1$

Let the equation of the circle be

$x^2+y^2+2gx+2fy+\lambda =0$

$(t,\frac{1}{t})$ be a point on the circle

$\therefore$ $t^2+\frac{1}{t^2}+2gt+2f\frac{1}{t}+\lambda =0$

$\Rightarrow t^4+2g{t}^3+\lambda t^2+2ft+1=0$

roots of the above equation are $a,b,c$ and $d$

$\therefore$ $abcd=1$