The locus of a point whose chord of contact with respect to the circle $x^2+y^2=4$ is a tangent to the hyperbola  xy=1 is a/an

 Let the point be (h, k). 

Then the equation of the chord of contact is hx + ky = 4. 

Since hx + ky - 4 is tangent to xy = 1, 

$x\left(\frac{4-hx}{k}\right)=1$

has two equal roots. Therefore, 

$\begin{array}{r}h{x}^2-4x+k=0\\ \text{ or }hk=4\end{array}$

Thus, the locus of (h, k) is xy =4. Hence, 

$c^2=4$