Find the equation of the tangent line to the curve (a lemniscate) $\displaystyle {2}{\left({x}^{{2}}+{y}^{{2}}\right)}^{{2}}={25}{\left({x}^{{2}}-{y}^{{2}}\right)}$ at the point $\displaystyle {\left({3},-{1}\right)}$.

The equation of this tangent line can be written in the form $\displaystyle {y}={m}{x}+{b}$
where $\displaystyle {m}$ is: Preview Question 6 Part 1 of 2  
and where $\displaystyle {b}$ is: Preview Question 6 Part 2 of 2