Math Is Fun Forum

infinitum

Member

Registered: 2008-08-14

Posts: 1

Please Help

Can anyone help me answer this question.

An ellipse has parametric equations
x= 3cos(angle)
y= 2sin(angle)
(i) find dy/dx at the point with parameter
(ii) find equation of the normal at the general point (3cos(angle),2sin(angle))

Thankyou and take care,

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Please Help

To differentiate a parametric equation, you differentiate both parts and then divide the y part by the x part.

dy/dθ = -3sinθ
dx/dθ = 2cosθ

∴ dy/dx = (-3/2)tanθ.

The gradient of the tangent to a curve at any point is equal to that curve's derivative at the point.
Also, the gradients of a curve's normal and tangent will always multiply to give -1, so that means you can find the gradient of a curve's normal at any point. Once you have that, it's easy enough to work out its y-intercept and that will give you the normal line's equation.

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Why did the vector cross the road?
It wanted to be normal.