$H_1:xy=c^2\text{ and }{H}_2:xy=k^2$ are two different hyperbolas. From a point on $H_1$, tangents are drawn to $H_2$.Area of the triangle formed by the chord of contact and the asymptote to $H_2$ is 

Equation of the chord of contact from $\left(ct,\frac{c}{t}\right)\text{ on }{H}_1$ $\text{ to }{H}_2\text{ is }\left(ct\right)x+\left(\frac{c}{t}\right)y=2k^2\text{. }$

Asymptote of $H_2$ are $x = 0$ and $y = 0$ and the chord meets

these asymptotes at A $\left(\frac{2k^2}{ct},0\right)\text{ and }B\left(0,\frac{2k^{2}t}{c}\right)$

Area of the required triangle is $\frac{1}{2}\left|\frac{2k^2}{ct}\right|\left|\frac{2k^{2}t}{c}\right|=\frac{2k^4}{c^2}$