Answer:
12. center: (2, -3); radius: 2; equation: (x -2)^2 +(y +3)^2 = 4
13. 47°
Explanation:
12. The standard form equation of a circle with center (h, k) and radius r is ...
(x -h)^2 +(y -k)^2 = r^2
The center is halfway between the extremes, so is halfway between 0 and 4 in the x-direction and halfway between -5 and -1 in the y-direction. That is, the center is at (2, -3).
The diameter is the difference of the extremes, so is 4-0 = 4. The radius is half that, so is 2. Now, we know (h, k) = (2, -3) and r=2, so we can write the equation as ...
(x -2)^2 +(y +3)^2 = 4
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13. The external angle where the secants meet is half the difference of the intercepted arcs: (142° -48°)/2 = 94°/2 = 47°.