## BMF96 2 years ago 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?

1. LogicalApple

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. |dw:1359140495765:dw|

2. BMF96

I don't completely understand. What is the final equation? x^2 + (y+3)^2 - 9?

3. BMF96

which seems to simplify to x^2 + y^2

4. LogicalApple

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.

5. BMF96

looks like a circle with the origin at -3

6. BMF96

and radius of 3

7. LogicalApple

Right. A circle centered at (0, -3) with radius 3. And that's all there is to it :)

8. BMF96

Right, Thanks!