Question

A curve, described by x^2 + y^2 + 8x = 0, has a point A at (−4, 4) on the curve.

Part A: What are the polar coordinates of A? Give an exact answer.
Part B: What is the polar form of the equation? What type of polar curve is this?
Part C: What is the directed distance when theta equals 5 pi over 6 question mark Give an exact answer.

Answer 1

Answer: Part A

Step-by-step explanation: In order to convert that rectangular coordinates into a polar one, we need to think of a right triangle whose hypotenuse is connecting the point to the origin.

So, we need to resort to some equations:

Thus, we need now to plug x=-4 and y=4 into that:

Note that we needed to add pi to the arctangent to adjust that point to the Quadrant.

Thus, the answer is: