Question

The graph of r = -10 cos θ has which of the following characteristics?

Answer choices are listed below.

Answer 1

Explanation:

If we convert

`r = - 10 \cos(x)`

to a Cartesian equation,

`{r}^(2) = - 10 r \: \cos(x)`

`{x}^(2) + {y}^(2) = - 10x`

`{x}^(2) + 10x + {y}^(2) = 0`

`{x}^(2) + 10x + 25 + {y}^(2) = 25`

`(x + 5) {}^(2) + {y}^(2) = 25`

So we have a circle with center (-5,0), with a diameter of 10.