Chapter 9 Quadratic Relations and Conic Sections - 9.5 Graph and Write Equations of Hyperbolas - 9.5 Exercises - Skill Practice - Page 645: 21

See below

The foci and vertices lie on the y-axis equidistant from the origin, so the transverse axis is vertical and the center is the origin. The foci are each 5 units from the center, so $c =12$. The vertices are each 1 unit from the center, so $a=7$. Find $b^2=c^2-a^2=12^2-7^2=95$ $b=\sqrt 95$ Because the transverse axis is vertical, the standard form of the equation is as follows: $$\frac{y^2}{49}-\frac{x^2}{95}=1$$