Partial Solutions for Appendix G
Michael Roy
See also: http://bcs.wiley.com/he-bcs/Books?action=resource&bcsId=
2257&itemId=0471472441&resourceId=8026
p
5. Plug in to our formulas for distance and midpoints: d = (−2 − (−7))2 + (−6 − (−4))2 =
√
29. Midpoint = ( −2+(−7)
, −6+(−4)
) = ( −9
2
2
2 , −5).
9. Use the distance formula
to show that the distance from each of the three
√
each is the same distance from the center,
listed points to (−2, 3) is 29. Since√
they all lie on the circle with radius 29.
23. Answers can be read off using the general equation for a circle. Note
that the first part, x2 + y 2 = 25 is equivalent to (x − 0)2 + (y − 0)2 = 25 Thus the
centers in (a) through (d) are (0, 0), (1, 4), (−1,
√ −3) (note these are negative),
and (0, −2). The corresponding radii are 5, 4, 5, and 1.
25. Plug in to our equation for a circle: (x − 3)2 + (y − (−2))2 = 42 , which
simplifies to (x − 3)2 + (y + 2)2 = 16.
33. Using algebra to complete the square, this simplifies to (x − 1)2 + (y −
2)2 = 4. 4 > 0, so this represents a circle with center (1, 2) and radius 2. If
you don’t recall how to complete the square, don’t worry about it: it probably won’t come up again. If you’re curious check http://en.wikipedia.org/
wiki/Complete_the_square.
39. Divide both sides by 9, so x2 + y 2 = 91 . 19 > 0, so this represents a circle
q
with center (0, 0) and radius 31 (note 19 = 31 ).
61, 63. See the graphs on Wiley. They’re using the formula x = −b
2a to
find the x-coordinate of the vertex and setting x = 0 and y = 0 to find the
y-intercept and x-intercepts.
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