C3 - Parametric equations

Hi,

I'm stuck on these two questions on parametric equations, and was hoping someone would be able to show me how to do them:

1) The parametric equations of a curve are x=t²+1/t, y=t²-1/t. Find the cartesian equation of this curve.

Answer: (x+y)(x-y)²=8

2) A curve has parametric equations x=cost, y=1/2sin2t for 0<=t=<2pi

Show that the cartesian equation of the curve is y²=x²(1-x²)

Thank you very much! :smile:

Reply 1

yusufu

sweet_gurl

Hi,

I'm stuck on these two questions on parametric equations, and was hoping someone would be able to show me how to do them:

1) The parametric equations of a curve are x=t²+1/t, y=t²-1/t. Find the cartesian equation of this curve.

Answer: (x+y)(x-y)²=8

xt - 1 = t^3 = yt +1
xt - yt = 2
t(x-y) = 2
t= 2/(x-y)

x = 4/(x-y)² + (x-y)/2

x -(x-y)/2 = 4/(x-y)²
(x+y)/2 = 4/(x-y)²
(x+y)(x-y)² = 8

Reply 2

NeilosRobbos

Q1 I'm probably being stupid and not seeing the answer.

Q2 =

x = cost y= 1/2 sin2t

y = cost sint (compound angle formulae x 1/2)

y = x sint
y/x = sint

sin^2 t + cos^2 t = 1

(y/x)^2 + (x)^2 =1

y^2 / x^2 = 1 - x^2

Y^2 = x^2(1 - x^2)