Step 1

Given polar equations:

r=3

\(\displaystyle{r}=-{4}{\cos{{\left({0}\right)}}}\)

Step 2

To find points of intersection of given polar equations:

\(\displaystyle-{4}{\cos{{\left({0}\right)}}}={3}\)

\(\displaystyle{\cos{{\left({0}\right)}}}=-\frac{{3}}{{4}}\)

\(\displaystyle{0}={{\cos}^{{-{1}}}{\left(-\frac{{3}}{{4}}\right)}}\)

\(\displaystyle{0}={138.6}^{{\circ}},{221.4}^{{\circ}}\)

Step 3

Therefore,

The points of intersection of the pair of polar equations are

\(\displaystyle{\left({3},{138.6}^{{\circ}}\right)}\)

\(\displaystyle{\left({3},{221.4}^{{\circ}}\right)}\)

Given polar equations:

r=3

\(\displaystyle{r}=-{4}{\cos{{\left({0}\right)}}}\)

Step 2

To find points of intersection of given polar equations:

\(\displaystyle-{4}{\cos{{\left({0}\right)}}}={3}\)

\(\displaystyle{\cos{{\left({0}\right)}}}=-\frac{{3}}{{4}}\)

\(\displaystyle{0}={{\cos}^{{-{1}}}{\left(-\frac{{3}}{{4}}\right)}}\)

\(\displaystyle{0}={138.6}^{{\circ}},{221.4}^{{\circ}}\)

Step 3

Therefore,

The points of intersection of the pair of polar equations are

\(\displaystyle{\left({3},{138.6}^{{\circ}}\right)}\)

\(\displaystyle{\left({3},{221.4}^{{\circ}}\right)}\)