A curve has parametric equations :

, where is a constant

(1) Show that the curve is symmetrical about the y-axis

(2) For ,find in terms of the coordinates of the point where the curve intersects itself.

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- June 25th 2010, 10:38 PMhookeParametric equations
A curve has parametric equations :

, where is a constant

(1) Show that the curve is symmetrical about the y-axis

(2) For ,find in terms of the coordinates of the point where the curve intersects itself. - June 26th 2010, 02:16 AMAckbeet
Ok, what ideas have you had so far?

- June 26th 2010, 02:17 AMmr fantastic
(1) x --> -x => t --> -t and t --> -t => y --> y therefore the function is even (symmetric about y-axis).

(2) You are trying to find a crunode: Crunode - Wikipedia, the free encyclopedia.

Note that crunodes occur at points where dy/dx has the indeterminant form 0/0. So get dy/dx, find the value of t for which dy/dx is indeterminant and then substitute this value of t into x = x(t) and y = y(t). (You know in advance that the point is a crunode but you should test it anyway). - June 26th 2010, 02:28 AMhooke
- June 26th 2010, 02:42 AMmr fantastic
- June 26th 2010, 02:58 AMhooke
- June 26th 2010, 07:54 AMHallsofIvy
Well, what else can it be? If the derivative were not indeterminant, then it would have

**one**"determinant" value and that would be the slope of**the**tangent line.

But mr fantastic was answering a different question, "why is 0/0 not "infinite?"(giving a vertical tangent). The answer to that is that limits such as , all involve fractions of the form "0/0" but different limits and so different "slopes". To have an infinite limit your fraction must be of the form "a/0" where a is not 0. - June 28th 2010, 03:21 AMhooke
- June 28th 2010, 03:58 PMmr fantastic