In Exercises 49–58, convert each rectangular equation to a pol...

Question

In Exercises 49–58, convert each rectangular equation to a polar equation that expresses r in terms of θ.

x² = 6y

Accepted Answer

Welcome back, everyone. Transform the rectangular equation X2 equals 31y into a polar equation expressing R in terms of data. There are 4 answer choices A R equals 31 divided by cosine squared theta, B 31 sin theta divided by cosine squared of theta, C 31 cosine theta divided by sin squared theta, and D 31 sin theta divided by cosine theta. So for this problem we want to recall that X can be expressed as R cosine of theta in polar coordinates and Y can be expressed as R multiplied by sine theta, and we want to substitute these into the given equation X2. Equals 31 Y. So if we square x, we're going to get R cosine theta squared. And this must be equal to 31 y, which is 31. Multiplied by our sin theta. Now let's simplify. Let's square the left hand side. This gives us r squared. Followed by cosine squared data and on the right hand side we still have 31 Rs data. Now let's notice that we have a common term which is R, so let's divide both sides by R. And since we have division, R cannot be equal to 0, right, because division by 0 is undefined. So on the right hand side we can cancel out r, and on the left hand side we can cancel out R and R squared, right? So this reduces to R. From here we get our cosine squared theta is equal to 31 sin theta, and finally we want to isolate R. So let's divide both sides by Cosine squared of theta. This allows us to eliminate cosine square of data on the left hand side. We also want to make sure that cosine squared of data is not equal to 0, once again, division by 0 is undefined, and we end up with R equals. 31 Sign theater Divided by cosine squared. Of the Now considering the answer choices, we can conclude that the correct answer to this problem corresponds to the answer choice of B. Thank you for watching.

In Exercises 49–58, convert each rectangular equation to a polar equation that expresses r in terms of θ.

x² = 6y

Key Concepts

Rectangular to Polar Coordinates

Polar Equation Format

Graphing Polar Equations

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