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Unformatted text preview: hat they must be a distance of r from the center. Therefore the points will have the following
coordinates. right most point : ( h + r , k )
left most point : ( h - r , k )
top most point : ( h, k + r )
bottom most point : ( h, k - r )
In other words all we need to do is add r on to the x coordinate or y coordinate of the point to get
the right most or top most point respectively and subtract r from the x coordinate or y coordinate
to get the left most or bottom most points.
Let’s graph some circles. Example 2 Determine the center and radius of each of the following circles and sketch the
graph of the circle.
(a) x 2 + y 2 = 1 [Solution]
(b) x 2 + ( y - 3) = 4 [Solution]
2 (c) ( x - 1) + ( y + 4 ) = 16 [Solution]
2 2 Solution
In all of these all that we really need to do is compare the equation to the standard form and
identify the radius and center. Once that is done find the four points talked about above and
sketch in the circle.
(a) x 2 + y 2 = 1
In this case it’s just x and y squared by themselves. The only way th...
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- Spring '12