Hello, Bushy!
Mr. F is absolutely correct!
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 two -intercepts.
Where is the other one? .Where is our error?
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 never equal Infinity, can it?
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.