Question #5e370

1 Answer
Douglas K.
Mar 26, 2017

The Standard Cartesian Form for the equation of a circle is:
#(x-h)^2+(y-k)^2=r^2" [1]"#
Where #(x,y)# is any point on the circle, #(h,k)# is the center, and #r# is the radius.

Explanation:

Given that the center is #(0,0)# we substitute this into equation [1] to obtain equation [2]:

#(x-0)^2+(y-0)^2=r^2" [2]"#

Substitute the point #(12-5)# into equation [2] and solve for r:

#(12-0)^2+(-5-0)^2=r^2#

#169 = r^2#

#r = 13#

Substitute 13 for r in equation [2]:

#(x-0)^2+(y-0)^2=13^2" [3]"#

Equation [3] is the equation of the specified circle.

Here is its graph:

graph{(x-0)^2+(y-0)^2=13^2 [-30, 30, -15, 15]}

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