# Write the equation of a circle centered at (3,4) with a radi

Write the equation of

a. a circle centered at (3,4) with a radius 5

(See attached file for full problem description)

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a. The equation for a circle is

(x - h)2 + (y - k)2 = r2

where h and k are the x- and y-coordinates of the center of the circle and r is the radius. So in this problem the equation for the circle centered at (3,4) and r = 5 is:

(x - 3)2 + (y - 4)2 = 25

b. Let y = ax + b. This line goes thru (-1,3) and (5,18) hence:

-a + b = 3 OR b = a +3

5a + b = 18

Substitute b = a + 3 into the above:

5a + a + 3 = 18

Hence 6a = 15 or a =15/6 =2.5

And therefore b = 5.5

The line has the form y = 2.5x + 5.5

c. Choose some point having coordinates (x,y). The distance between this point and (-5,4) is given by:

The distance between point (x,y) and (3,16) is given by

Equating these distances, since the point is to be equidistant from the two given points, we have:

=

Squaring both sides, we have:

Reference:

http://www.tpub.com/math2/10.htm

Substitute one into the other:

Hence the points of intersection are (0.5,0.87) and (-0.5,-0.87)

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#### Solution Summary

The solution provides detailed and step-by-step instructions, including drawings, in 10 pages of Word and Excel on how to solve these algebra problems.