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We consider a family of analytic and normalized functions that are related tothe domains $\mathbb{H}(s)$, with a right branch of a hyperbolas $H(s)$ as aboundary. The hyperbola $H(s)$ is given by the relation $\frac{1}{\rho}=\left(2\cos\frac{\varphi}{s}\right)^s\quad (0<s\le 1,\ |\varphi|<(\pi s)/2$). Wemainly study a coefficient problem of the families of functions for which$zf'/f$ or $1+zf''/f'$ map the unit disk onto a subset of $\mathbb{H}(s)$. Wefind coefficients bounds, solve Fekete-Szeg\"{o} problem and estimate theHankel determinant.

Coefficients problems for families of holomorphic functions related to hyperbola