Answer:
a)
<em>h = 1
</em>
<em>k = 7
</em>
<em>R = 9</em>
b) Initial point: (1,16)
c) Terminal point : (1 -2)
<em>The path is traced counterclockwise</em>
Step-by-step explanation:
We have the parametric curve
x(t) = 1+9cos(t)
y(t) = 7+9sin(t)
with π/2 ≤ t ≤ 3π/2
a)
We can see that
x-1 = 9cos(t)
y-7 = 9sin(t)
hence
so
h = 1
k = 7
R = 9
We notice that the curve is part of a circumference with radio 9 and center (1,7)
b)
The initial point is obtained when t = π/2
x(π/2) = 1+9cos(π/2) = 1
y(π/2) = 7+9sin(π/2) = 7+9 = 16
The initial point is then (1,16)
c)
The terminal point is obtained when t = 3π/2
x(3π/2) = 1+9cos(3π/2) = 1
y(3π/2) = 7+9sin(3π/2) = 7-9 = -2
The final point is (1,-2)
<em>The path is the part of the circumference with center (1,7) and radio 9 </em><em>traced counterclockwise</em><em> from (1,16) to (1,-2)</em>