Question

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

Answer 1

Step-by-step 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.