# Thread: help on parametr equation i cant do it at all

1. ## help on parametr equation i cant do it at all

x=Acos^3t , y= Asin^3t

where A is a positive constant and 0<t<0.5pie

1 express dy/dx in terms of t

2 show that equation of the tangent to the curve at the point with parameter t is

Xsint + ycost = Asint times cost

extra question based on this

hence show that, if tangent meets the x axis at X and the Y axis at Y then the length of XY is always equal to A

2. Originally Posted by vserian
x=Acos^3t , y= Asin^3t

where A is a positive constant and 0<t<0.5pie

1 express dy/dx in terms of t

2 show that equation of the tangent to the curve at the point with parameter t is

Xsint + ycost = Asint times cost

extra question based on this

hence show that, if tangent meets the x axis at X and the Y axis at Y then the length of XY is always equal to A
$\displaystyle \frac{dy}{dx}=\frac{dy}{dt}\frac{dt}{dx}$

Now differentiate the first equation with respect to $\displaystyle x$ to find $\displaystyle \frac{dt}{dx}$ and the second by $\displaystyle t$ to find $\displaystyle \frac{dy}{dt}$ and the first part is done.

CB