If (x+2)^2+(y-5)^2=25 is the equation of a circle, which statement describes the circle's graph?

a) the center of the circle is (2,5), and the circle's radius is 25.

b) the center of the circle is (-2,5), and the circle's radius is 5.

c) the center of the circle is (2,-5), and the circle's radius is 5.

d) the center of the circle is (-2,-5), and the circle's radius is 5.

B

Step-by-step explanation:

The standard form of a circle is

where h and k are the coordinates of the center of the circle and the radius is squared.  The radius is easy...take the square root of 25 to get that the radius is 5.  Since the pattern for the standard form is "x-" and "y-", if (x+2)^2 is the horizontal placement of the center, it actually was originally written as (x-(-2))^2, so the h coordinate is -2.  Same goes for the vertical movement of the center.  (y-(5))^2 means that the k coordinate is a positive 5.

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explanation

the graph has a slope of 1/3 because each time you move up 1, you go to the right 3. so, slope = rise/run = 1/3. we can cross choice a off the list since we want a slope of 3, rather than 1/3.

the first table shown has a slope of -3. this is because the rise is -6 and the run is 2, so slope = rise/run = -6/2 = -3. note how x increases by 2 each time (run) and y drops by 6 each time (rise). choice b can be eliminated.

the second table has a slope of 3. each time x goes up by 1, the y values increase by 3. slope = rise/run = 3/1 = 3. alternatively you can use the slope formula to prove that the slope is 3 here. use any two rows of values to generate the two points. choice c is one of the answers

the third table also has a slope of 3. let's use the slope formula to prove as such. i'm going to use the first two rows of the table. so i'll use the two points (2,1) and (5,10)

m = slope

m = (y2-y1)/(x2-x1)

m = (10-1)/(5-2)

m = 9/3

m = 3 so we get a slope of 3

choice d is the other answer

h/o/e/s mad

step-by-step explanation:

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