r = -6 sinθ
Part I: Multiply both sides of this equation by r and use the fact that to rewrite this equation in terms of x and y.
I got x^2 + y^2 = -6y
Part II: Complete the square to produce the final equation.
Part III: Using only your answer to part II, what shape does this graph make?
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So you want to move 6y over to the left side to obtain:
x^2 + y^2 + 6y = 0
Then complete the square for the y variables.
To do this, you'd take 6, divide it by 2, then square the result. You should end up with 9.
I don't completely understand. What is the final equation?
x^2 + (y+3)^2 - 9?
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No, you simply completed the square. There is no way to simplify it to x^2 + y^2.
However, if you remember, your equation is now equal to 0.
x^2 + (y + 3)^2 - 9 = 0
Add 9 to both sides and see if you recognize this type of equation.
looks like a circle with the origin at -3
and radius of 3
Right. A circle centered at (0, -3) with radius 3. And that's all there is to it :)