1. ## Parametric Equations

Thanks to those who realised that I had typed the question wrong... here is the correct version
Please may someone help me solve this question:

A curve is defined by the parametric equations
x = 5 + 2cosθ, y = 3cos2θ

a) Show that dy/dx = 6cosθ
b) Verify that 2(y+3) = 3(x-5)^2 is a cartesian equation for the curve

Thank you so much !

2. Originally Posted by racheltllong
Please may someone help me solve this question:

A curve is defined by the parametric equations
x = 5 + cos2θ, y = 3cos2θ

a) Show that dy/dx = 6cosθ
b) Verify that 2(y+3) = 3(x-5)^2 is a cartesian equation for the curve

Thank you so much !
Please check your question; what you are asked to show appears not to correspond to the parametric equation given.

This is assuming that the equation is supposed to be:

$x = 5 + \cos^2(\theta),\ y = 3\cos^2(\theta)$,

or even:

$x = 5 + \cos(2\theta),\ y = 3\cos(2\theta)$.

RonL

3. You seem to have an error in your problem as written. Note that from what you provided:

$
x = 5 + \cos (2 \theta)
$

$
\cos (2 \theta) = x - 5
$

$
y = 3 cos (2 \theta) = 3 (x-5) = 3x -15.
$

Hence dy/dx = 3, not $6 cos(\theta)
$