- #1

chwala

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- Homework Statement
- Find the equation of the normal to a curve given parametric equations;

##x=t^3, y=t^2##

- Relevant Equations
- Parametric equations

This is a text book example- i noted that we may have a different way of doing it hence my post.

Alternative approach (using implicit differentiation);

##\dfrac{x}{y}=t##

on substituting on ##y=t^2##

we get,

##y^3-x^2=0##

##3y^2\dfrac{dy}{dx}-2x=0##

##\dfrac{dy}{dx}=\dfrac{2x}{3y^2}##

at points ##(-8,4)##

##\dfrac{dy}{dx}=\dfrac{-1}{3}##

...the rest of the steps to required solution will follow...

...any insight is welcome.

Alternative approach (using implicit differentiation);

##\dfrac{x}{y}=t##

on substituting on ##y=t^2##

we get,

##y^3-x^2=0##

##3y^2\dfrac{dy}{dx}-2x=0##

##\dfrac{dy}{dx}=\dfrac{2x}{3y^2}##

at points ##(-8,4)##

##\dfrac{dy}{dx}=\dfrac{-1}{3}##

...the rest of the steps to required solution will follow...

...any insight is welcome.

Last edited: