Question

How do you differentiate the following parametric equation: `x(t)=-t-2, y(t)= t^2/(-t+4`?

Answer 1

`(dy)/(dx)=(t(t-8))/(4-t)^2`

Explanation:

Differential of a parametric of the type `y=y(t)` and `x=x(t)` is given by

`(dy)/(dx)=((dy)/(dt))/((dx)/(dt))`

Here `(dy)/(dt)=((-t+4)xx2t-t^2(-1))/(-t+4)^2`

= `((8t-2t^2)+t^2)/(-t+4)^2=(t(8-t))/(4-t)^2`

As `x=-t-2`, `(dx)/(dt)=-1`

Hence `(dy)/(dx)=(t(8-t))/(4-t)^2xx(-1)=(t(t-8))/(4-t)^2`