In Exercises 59–74, convert each polar equation to a rectangular ...

Question

In Exercises 59–74, convert each polar equation to a rectangular equation. Then use a rectangular coordinate system to graph the rectangular equation.

r = 12 cos θ

Accepted Answer

Transform the given polar equation into a rectangular equation. Use the resulting equation to draw the graph where we have R equals eight cosine data. And we're given a coordinate plane to graph our equation on. So you want to transform into a rectangular equation, we could use a couple of substitutions. We know since we have a cosign data, cosign data will be X divided by R. We also know R squared will be X squared plus Y squared. Let's first replace R cosine data. If R equals eight X divided by R instead multiply both sides by R to give us R squared equals A X. Finally, we move everything to one side by subtracting eight X, we get R squared minus eight X equals zero. Now, since we have an R squared, we can use our substitution X squared plus Y squared minus eight X equals zero. Now this is taken the form of an equation of a circle. We'll find the equation by circle by completing the square, we move X squared and eight X by each other. Our negative eight X plus Y squared equals zero. Now we in the square, we will take the number, multiplying our X divide it by two and square it, we add the sum to both sets, which in our case, this is 16, we have X squared minus eight X plus 16. And then plus Y squared is equals to zero plus 16. On the right, since we add it to one side, we have to add it to the other side. We can now factor our X squared minus eight X plus 16. We should get X minus four square. Bring down our Y squared set, it equals to 16. We have the equation of a circle where the center occurs as a 0.40. And our radius is four. We can plot this on our graph. Our center is that 40 radius of four. So we can plot points four out from the center and we can finally create our circle. OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

In Exercises 59–74, convert each polar equation to a rectangular equation. Then use a rectangular coordinate system to graph the rectangular equation. r = 12 cos θ

Key Concepts

Polar Coordinates

Rectangular Coordinates

Conversion Formulas

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