Solving a Parametric Position Equation
A particle moves along a path with positions given by
$$x(t)=\frac{t^2+4*t+4}{t+2}$$ and
$$y(t)=\sqrt{\frac{9*t^2+12*t+4}{t^2+4*t+4}}.$$
Find the value of $$t$$ for which $$x(t)+y(t)=8.$$
A particle moves along a path with positions given by
$$x(t)=\frac{t^2+4*t+4}{t+2}$$ and
$$y(t)=\sqrt{\frac{9*t^2+12*t+4}{t^2+4*t+4}}.$$
Find the value of $$t$$ for which $$x(t)+y(t)=8.$$