<s>[INST] Which conic is represented by $r = a \cos \theta$ The polar equation $r = a \cos \theta$  represents which conic?
 [/INST] Multiply both sides by $r$ to get $r^2 = a r \cos \theta$. Then we use the substitution $r^2 = x^2 + y^2$ and $r \cos \theta = x$ to get $x^2 + y^2 = ax$. Then we get $\displaystyle \left(x - \frac{a}{2}\right)^2 + y^2 = \frac{a^2}{4}$. Looks like it's a circle.
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