Question Number 131674 by liberty last updated on 07/Feb/21
![Given y=f(x) satisfies (dy/dx) + ((√((x^2 −1)(y^2 −1)))/(xy)) = 1 lies at point (1,1) and ((√2) ,k). find k .](https://www.tinkutara.com/question/Q131674.png)
$$\mathrm{Given}\:\mathrm{y}=\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{satisfies}\: \\ $$$$\:\frac{\mathrm{dy}}{\mathrm{dx}}\:+\:\frac{\sqrt{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{1}\right)\left(\mathrm{y}^{\mathrm{2}} −\mathrm{1}\right)}}{\mathrm{xy}}\:=\:\mathrm{1}\: \\ $$$$\mathrm{lies}\:\mathrm{at}\:\mathrm{point}\:\left(\mathrm{1},\mathrm{1}\right)\:\mathrm{and}\:\left(\sqrt{\mathrm{2}}\:,\mathrm{k}\right). \\ $$$$\mathrm{find}\:\mathrm{k}\:. \\ $$