Chapter 10: Q. 9 (page 701)

Find a polar equation for the circle with center at the point $(0, 4)$ and radius 4. Graph this circle.

Short Answer

Expert verified

The equation is $r = 8 \sin θ$ and the graph is

Step by step solution

Step 1. Given Information

The given center is $(0, 4)$ and radius is 4.

Step 2. Explanation

The equation has a circle in rectangular cartesian coordinates is given below,

${(x - h)}^{2} + {(y - k)}^{2} = a^{2}$

The circle has a radius 4 units and center at $(0, 4)$ ,

${(x - 0)}^{2} + {(y - 4)}^{2} = 4^{2} x^{2} + y^{2} - 8 y = 0$

Thus, equation of circle in rectangular coordinates is $x^{2} + y^{2} - 8 y = 0$

Substitute the values $x = r \cos θ, y = r \sin θ$ to get the polar form of the equation.

${(r \cos θ)}^{2} + {(r \sin θ)}^{2} - 8 (r \sin θ) = 0 r^{2} - 8 r \sin θ = 0 r = 8 \sin θ$

And the graph is as follows,

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Find a polar equation for the circle with center at the point $(0, 4)$ and radius 4. Graph this circle.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Explanation

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Find a polar equation for the circle with center at the point (0,4)and radius 4. Graph this circle.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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Study anywhere. Anytime. Across all devices.

Find a polar equation for the circle with center at the point $(0, 4)$ and radius 4. Graph this circle.