Question

If the curve $xy=c(c>0)$ and the circle $x^2+y^2=1$ touches at two points, then distance between their points of contacts is unit

Answer 1

Equation of normal at $P(x_1,y_1)$ will be
$x{x}_1-y{y}_1=x_1^2-y_1^2$
Now this is also a normal to
$x^2+y^2=1$
$\because$ both the curves are symmetric about line $x+y=0$
Hence normal at $P$ will also pass through $Q$
$\therefore PQ$ is the diameter of the given circle
$\Rightarrow PQ=2$ unit