Homework SourseWhen you start with the ellipse xa2 yb2 r2 on xypaper and
When you start with the ellipse
(x/a)^2 + (y/b)^2 = r^2
on xy-paper and you go to uv-paper using
u[x, y] = x/a, and
v[x, y] = y/b,
then the xy-paper ellipse plots out as the uv-paper circle
u^2 + v^2 = r^2.
On uv-paper, the area enclosed by this circle measures out to
Pi r^2 square units.
What is the area conversion factor Axy[u,v]?
Answers:
A. a^2 + b^2
B. (x/a)(y/b)
C. Cannot calculate without knowing a and b.
D. a b
E. None of the above.
(x/a)^2 + (y/b)^2 = r^2
on xy-paper and you go to uv-paper using
u[x, y] = x/a, and
v[x, y] = y/b,
then the xy-paper ellipse plots out as the uv-paper circle
u^2 + v^2 = r^2.
On uv-paper, the area enclosed by this circle measures out to
Pi r^2 square units.
What is the area conversion factor Axy[u,v]?
Answers:
A. a^2 + b^2
B. (x/a)(y/b)
C. Cannot calculate without knowing a and b.
D. a b
E. None of the above.
Solution
Since we are told that:
u=x/a and v=y/b,
we can easily find that:
x=au and y=bv
Therefore, for to convert area of x*y we have
Axy=A(au*bv)=A(ab*uv)=Aab(uv)
Therefore, the answer is d.
![When you start with the ellipse (x/a)^2 + (y/b)^2 = r^2 on xy-paper and you go to uv-paper using u[x, y] = x/a, and v[x, y] = y/b, then the xy-paper ellipse plo](/WebImages/19/when-you-start-with-the-ellipse-xa2-yb2-r2-on-xypaper-and-1038019-1761538851-0.webp "When you start with the ellipse (x/a)^2 + (y/b)^2 = r^2 on xy-paper and you go to uv-paper using u[x, y] = x/a, and v[x, y] = y/b, then the xy-paper ellipse plo")
