Convert x² + (y + 8)² = 64 to a polar equation that expresses ...

Question

Convert x² + (y + 8)² = 64 to a polar equation that expresses r in terms of θ.

Accepted Answer

For the given equation X plus 11 squared plus Y squared equals 1 converted into a polar equation. And we have four possible answers here all with R equals and then some function in terms of theta. Now to solve this, we need to make use of our substitutions. We have two substitutions where we have X equals R cosine data and Y equals our sign of data. We can use these substitutions in our equation. You will get R cosign data plus squared plus our sign data squared equals 1 21. Now we can expand our R cosine data plus 11 square. We will get R squared cosine squared data plus 22 our cosine data plus 1 21 and then plus R squared sine squared data equals 1 21. Now we need to solve for art. Let's first move our 1 21 over to the other side by subtracting. This gives us R squared cosine squared data plus 22 R cosine data plus R squared sine squared data an hour equals zero. No, we notice here we have an R squared cosine squared plus an R squared sine squared one thing we know is that we can factor out the R squared and get one of our known trick identities cosine squared data and sine squared data. So I will write this as R squared cosine squared data plus sign square data plus 22 are cosine theta equals zero. No, our pythagorean identity tells us that cosine squared plus sine squared is equivalent to one, meaning we have R squared plus 22 R cosine data equals zero. Now we still want R by itself. So we will factor out an R here. We hit R multiplied by R plus assign data equals zero. Now we can split both of these up since they both equal zero into R equals zero and R plus 22 cosine data equals zero. Finally, we can subtract 22 cosine data to get R equals negative 22 cosine data which we notice in our problem, this corresponds to answer B. So our answer is R equals 22 negative 22 cosine data. OK? I hope to help you solve the problem. Thank you for watching. Goodbye.

Convert x² + (y + 8)² = 64 to a polar equation that expresses r in terms of θ.

Key Concepts

Polar Coordinates

Equation of a Circle in Cartesian Form

Substitution and Simplification in Polar Form

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