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Serjik [45]
3 years ago
14

Find parametric equations for the path of a particle that moves along the circle x2 + (y − 3)2 = 16 in the manner described. (en

ter your answer as a comma-separated list of equations. let x and y be in terms of t.) (a) once around clockwise, starting at (4, 3). 0 ≤ t ≤ 2π.
Mathematics
1 answer:
sveticcg [70]3 years ago
5 0

Answer:

x(t) = 4 cos(-t)\\y(t) = 4 sin(-t) + 3\\

and t ∈ [0,2π]

Step-by-step explanation:

The standard equation for circle is:

(x-h) ^2 + (y-k)^2 = r^2

Comparing our equation with standard

x^2 + (y-3)^2 =16

h= 0,

k= 3

r= 4 (as in standard r², so r =√ r²)

Required:

Parametric equations of the circle

Formula:

x = r cos(t) + h\\y= r cos(t) +k

Putting values of r and h and k we get

x= 4 cos(t) + 0 \\x= 4 cost(t) \\y= 4 sin(t) + 3

As we need to start the object at (4,3)

x(0) = 4 and y(0) = 3

and the period is 2π

As the rotation is starting clock wise we will invert the value of t i.e -t

x(t) = 4 cos(-t)\\y(t) = 4 sin(-t) + 3\\

and t ∈ [0,2π]

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