Question 123988
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Discussion
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The equation for a circle with center (h,k) and radius r is:


{{{(x-h)^2+(y-k)^2=r^2}}}


The distance between the center of a circle and any point on the circle is
the measure of the radius.  To calculate the distance between two points, use
the distance formula:


{{{d=sqrt((x[1]-x[2])^2+(y[1]-y[2])^2)}}}
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Solution
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You are given the center of the circle as (-3,4) so we know that
h=-3 and 
k=4

The circle radius is the distance from (-3,4) to (10, 4).  In this case, you
don't actually have to use the distance formula because the y-coordinates of
the two points are equal and the distance formula degenerates to the square
root of the square of the difference in the x-coordinates.  In other words,
the distance is found by the absolute value of the difference in the
x-coordinates.


{{{abs(-3-10)=abs(-13)=13}}}


Now we have sufficient information to write the desired equation:


{{{(x-(-3))^2+(y-4)^2=13^2}}}


You can simplify and put the equation in standard form, if you like, but unless
instructed to do so, I wouldn't go to all that effort.
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