Question

Determine which equation is belongs to the graph of the limacon curve below.

[-5,5] by [-5,5]
a. r= 4 + cose
b. r= 2 + 3 cose
c. r= 3 + 2 cose
d. r= 2 + 2 cose

Answer 1

Correct option is C )
`r=3+2\,cos\theta`

Explanation:

Limacons are polar functions of the type:

`r=a\pm\,b\,cos\theta`

`r=a\pm\,b\,sin\theta`

Where
`|(a)/(b)|<1\,or\,1<|(a)/(b)|<2\,or\,|(a)/(b)|$\geq$2`

In provided options part (a) and (d) constants 'a' and 'b' does not satisfied the condition,

in part (b) and (c) both satisfies the condition but in part (b) we get loop inside the sketch.

so,
`r=3+2\,cos\theta` satisfies the condition of graph.

hence correct option is c )
`r=3+2\,cos\theta` .

Answer 2

c. 3 + 2 cosθ

Explanation:

a = 3, b = 2

Since a > b, 1 <
`(3)/(2)` <2

we get a dimpled limacon.