Consider the family of curves described by the parametric equations x = a cos t + h , y = b sin t + k 0 ≤ t ≤ 2 π where a ≠ 0 and b ≠ 0. Describe the curves in this family if (a) h and k are fixed but a and b can vary (b) a and b are fixed but h and k can vary (c) a = 1 and b = 1 , but h and k vary so that h = k + 1.
Consider the family of curves described by the parametric equations x = a cos t + h , y = b sin t + k 0 ≤ t ≤ 2 π where a ≠ 0 and b ≠ 0. Describe the curves in this family if (a) h and k are fixed but a and b can vary (b) a and b are fixed but h and k can vary (c) a = 1 and b = 1 , but h and k vary so that h = k + 1.
Consider the family of curves described by the parametric equations
x
=
a
cos
t
+
h
,
y
=
b
sin
t
+
k
0
≤
t
≤
2
π
where
a
≠
0
and
b
≠
0.
Describe the curves in this family if
(a) h and k are fixed but a and b can vary
(b) a and b are fixed but h and k can vary
(c)
a
=
1
and
b
=
1
,
but h and k vary so that
h
=
k
+
1.
Consider the family of curves described by the parametric equations x = a cos t + h, y = b sint + k. (0 ≤ t < 2π) where a ≠ 0and b ≠ 0. Describe the curves in this family if (a) h and k are fixed but a and b can vary (b) a and b are fixed but h and k can vary (c) a = 1and b = 1, but h and k vary so that h= k + 1.
find the parametric equations for the line segment from (-2,5) to (7,-1) your equation for x should not be x=t. define your interval for the parameter t.
Eliminate the parameter in the parametric equations x =7+ sint, y = 2 + sint, for 0sts
and describe the curve, indicating its positive orientation. How does this curve differ from the curve x = 7+ sin t, y = 2 + sin t, for
7stsn?
Chapter 10 Solutions
Calculus Early Transcendentals, Binder Ready Version
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Fundamental Theorem of Calculus 1 | Geometric Idea + Chain Rule Example; Author: Dr. Trefor Bazett;https://www.youtube.com/watch?v=hAfpl8jLFOs;License: Standard YouTube License, CC-BY