Answer:
Solution : ( - 8, - 5π/3 )
Step-by-step explanation:
There are four cases to consider here, the first two with respect to r > 0, the second two with respect to r < 0. For r < 0 we have the coordinates ( - 8, 60° ) and ( - 8, - 300° )
. - 300° in radians is - 5π/3, and hence our solution is option d. But let me expand on how to receive the coordinates. Again r is the directed distance from the pole, and theta is the directed angle from the positive x - axis.
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So when r is either negative or positive, we can tell that this point is 8 units from the pole. Therefore - r = - 8 in both our second cases ( we are skipping the first two cases for simplicity ). For r < 0 the point will lay on the ray pointing in the opposite direction of the terminal side of theta.
Our first coordinate is ( - 8, 60° ). Theta will be 2 / 3rd of 90 degrees, or 60 degrees, for - r. Respectively the remaining degrees will be negative, 360 - 60 = 300, - 300. Our second point for - r will thus be ( - 8, - 300° )
. - 300° = - 5π/3 radians, and our coordinate will be ( - 8, - 5π/3 ).
<u>Answer</u>
Center: (1,-12)
Radius: 5
<u>Work</u>
+
-2x+24y+120=0 (Subtract 120 on both sides and rearrange)
-2x++24y=-120 (Then divide 2 by 2 and square it. Do the same for 24.)
-2x+1++24y+144=-120+1+144 (You have to add the same numbers on both sides)
(Simplify)
So you would put (1,-12); r=5
0 is the answer! U can type it in the calculator
