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.

y² = 6x

Accepted Answer

Welcome back everyone to another video. Transform the given rectangular equation into a polar equation. Y2 is equal to 117 X and we're given 4 answer choices A says, R equals 117. The divided by cosine squared theta, B 117 cosine squared theta, C 117 divided by sin squared of theta, and D, 117 cosine theta divided by sin squared of theta. So for this problem, let's recall the relationship between rectangular coordinates and polar coordinates. First of all, X is equal to R multiplied by cosine of theta and Y equals to R sine theta. So what we're going to do is simply substitute these into the given equation. First of all, we have Y2d on the left hand side. So we're going to write R sine theta in polar coordinates. This is going to be squared and this must be equal to 117 multiplied by X and X is R cosine theta. Now let's square the left hand side. This gives us R squared, followed by sin squared of data. On the right hand side we have 117 multiplied by our cosine data. And now we can divide both sides by R as long as it is not equal to 0, right? So let's divide both sides by R. This cancels out the r on the right hand side, and we also cancel out the square on the left hand side. Let's make sure that R is not equal to 0, and this gives us r. Sign Squared of data is equal to 117 cosine of data. And from here we can divide both sides by sine squared of data, right? So are It's going to be equal to, now, let's show the step. First of all, we're going to add the fraction sign to show the division. We're dividing both sides by side squared of theta. Once again, Sin squared of data cannot be equal to 0 because division by 0 is going to be undefined. And we get R equals. We can cancel out Sine squared data on the left hand side. And now on the right hand side we end up with. 117. Cosine of theta. Divided by sin squared of theta. Now considering the answer choices, we can see that the correct answer choice to this problem corresponds to the answer choice in D. Thank you for watching.

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

y² = 6x

Key Concepts

Rectangular to Polar Coordinates

Polar Equation Format

Graphing Polar Equations

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