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Chapter 9: Q.46 (page 747)

Graph the cardioids r=1+cos胃,r=2(1+cos胃),andr=3(1+cos胃)in the same polar coordinate system. What are the relationships among these three graphs? How does changing the constant kin the graph of the cardioidr=k(1+cos胃) affect the graph? What happens when k<0?

Short Answer

Expert verified

The graph is :

Step by step solution

01

Step 1. Given Information.

The given curves are :

r=1+cos胃,r=2(1+cos胃),andr=3(1+cos胃).

02

Step 2. Graphically.

The graph of the curves will be :

03

Step 3. Theoretically.

The given equations are :

r=k1+cos胃

In equations, the sign+and-affects the direction of the cardioid. Changing the value of k changes the size of the cardioid but does not affect its shape. The larger the value of k, the larger the resulting cardioid. If the value of k<0 , then smaller will be the cardioid.

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Most popular questions from this chapter

Each of the integrals or integral expressions in Exercises 38-44represents the area of a region in the plane. Use polar coordinates to sketch the region and evaluate the expressions.

Sketch the graphs of the equations

r=21+2cos胃and r=21+2sin胃

What is the relationship between these graphs? What is the eccentricity of each graph?

Use Cartesian coordinates to express the equations for the parabolas determined by the conditions specified in Exercises 22鈥�31.

r=伪1+cos胃

Use Cartesian coordinates to express the equations for the parabolas determined by the conditions specified in Exercises 22鈥�31.

directrixx=-1,focus(2,5)

Use Cartesian coordinates to express the equations for the hyperbolas determined by the conditions specified in Exercises 38鈥�43.

foci(0,卤4), directricesy=卤2
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