More general, consider the ellipse . One parametric representation of is . Let be the point , the map from to is bijective ; on the other hand, the map from to is also bijective. Then, the map from to is bijective from to except for the point ; that is, except for the point . As a consequence, a parametric representation of is:
Hello, pikachu26134!
Eliminate the parameter and find a Cartesian equation.
. .
Did you get Fernando's hint?
. .
. .
Add: .
m . . .
m . . .
We have a circle with radius 1 and its center at the origin.
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
I've posed this puzzle before, but it's worth repeating.
Where are the x-intercepts?
When
Then: .
The x-intercepts are: .
Where are the y-intercepts?
When
Then: .
There is one y-intercept: .
. . Where is the other one?