Step-by-step explanation:
If we convert
[tex]r = - 10 \cos(x) [/tex]
to a Cartesian equation,
[tex] {r}^{2} = - 10 r \: \cos(x) [/tex]
[tex] {x}^{2} + {y}^{2} = - 10x[/tex]
[tex] {x}^{2} + 10x + {y}^{2} = 0[/tex]
[tex] {x}^{2} + 10x + 25 + {y}^{2} = 25[/tex]
[tex](x + 5) {}^{2} + {y}^{2} = 25[/tex]
So we have a circle with center (-5,0), with a diameter of 10.
