Q. 4TB Parametric equations for a circl... [FREE SOLUTION]

Chapter 11: Q. 4TB (page 859)

Parametric equations for a circle: Find parametric equations whose graph is the circle with radius 蚁 centered at the point (a, b) in the xy-plane such that the graph is traced counterclockwise k > 0 times on the interval [0, 2蟺] starting at the point(a + 蚁, b).

Short Answer

Expert verified

The parametric equation of the circle is $\begin{array}{r} x = a + 蚁 \cos t \\ y = b + 蚁 \sin t \end{array}\} 0 鈮� t 鈮� 2 蟺 .$

Step by step solution

Step 1. Given Information.

It is given that the circle is centered at the the point $(a, b)$ with radius $蚁$ and the graph is traced counterclockwise $k > 0$ times with a starting point $(a + 蚁, b) .$

Step 2. Find the parametric equation for a circle.

It is given that the circle is centered at the point $(a, b)$ with the radius $蚁 .$ Thus, the parametric equation of a circle of center and radius is:

$x = a + 蚁 \cos t y = b + 蚁 \sin t$

Now, the graph is traced counterclockwise $k > 0$ times with a starting point role="math" localid="1649647969945" $(a + 蚁, b) .$ Thus, the parametric equation of the circle is:

$\begin{array}{r} x = a + 蚁 \cos t \\ y = b + 蚁 \sin t \end{array}\} 0 鈮� t 鈮� 2 蟺 .$

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91影视

Parametric equations for a circle: Find parametric equations whose graph is the circle with radius 蚁 centered at the point (a, b) in the xy-plane such that the graph is traced counterclockwise k > 0 times on the interval [0, 2蟺] starting at the point(a + 蚁, b).

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Find the parametric equation for a circle.

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