Mathematics

Problem

Which of the following conditions must be satisfied for the tangent lines to a smooth parametric curve

x=f(t),\,y=g(t)

at the parameter values

t_1

and

t_2

to be perpendicular? a)

\displaystyle \frac{dy}{dx}(t_1)\,\frac{dy}{dx}(t_2)=1

\displaystyle \frac{dy}{dt}(t_1)\,\frac{dy}{dt}(t_2)=-1

\displaystyle \frac{dy}{dx}(t_1)\,\frac{dy}{dx}(t_2)=-1

\displaystyle \frac{dy}{dx}(t_1)=-\frac{dy}{dx}(t_2)