Related questions with answers
(I am assuming that the "origin" was meant to be the point ; since the circle is in the plane , it is impossible for it to contain the point .)
Since it is in the plane which is parallel to the -plane, for now we can treat the circle as if it was in the -plane. Therefore, its equation is
where is its center, and is its radius.
Thus, from the text of the exercise, :
It contains the point , so we plug in , to find :
Therefore, the full equation of this circle is
For the circle with the center and the radius , the parametric representation is . Therefore, here we have that the parametric representation is
Truly, plug this into the LHS of (1):
So, truly holds.
Finally, for now we only have and coordinates in the parametric representation, so we must remember to include in the parametric representation of this circle:
Recommended textbook solutions
More related questions