I have this example that I found quite easy

using I concluded that

But anyone shed some light on this one?

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- September 5th 2010, 08:04 PMBushyCartesian Equation for a particle path.
I have this example that I found quite easy

using I concluded that

But anyone shed some light on this one?

- September 6th 2010, 03:07 AMmr fantastic
- September 6th 2010, 08:32 AMSoroban
Hello, Bushy!

Mr. F is absolutely correct!

Quote:

This problem involves one of my favorite "puzzles".

I can't resist sharing it, so I*must*solve the problem . . .

We have: .

Square the equations: .

Add:.

Hence, we have: .

This is a circle centered at the Origin with radius 1.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Here's the puzzle . . .

To find the -intercepts, let and solve.

In [1], let .

Then: .

The -intercepts are: .

. . We already knew that, didn't we?

To find the -intercepts, let and solve.

In [2], let .

Then: .

The -intercept is: .

But we know that the circle has-intercepts.*two*

Where is the other one? .Where is our error?

- September 6th 2010, 03:38 PMBushy
- September 6th 2010, 08:12 PMmr fantastic
- September 7th 2010, 09:57 AMSoroban

Mr. F has a great approach!

Here's an algebraic explanation.

We have: .

To find the -intercepts, find the value(s) of which produces .

We found one value, , which gave us:

What is the other value?

Consider letting grow*extremely large.*

We have: .

Hence, when "equals" Infinity.

Hence, when "equals" Infinity.

Therefore, when "equals" Infinity,

. . we have the other -intercept: .

Of course, can neverInfinity, can it?*equal*

The graph of the parametric equations is a unit circle

. . centered at the Origin with a "hole" at (-1, 0).

Okay, okay, I'm busted . . . It was a*trick question.*