SOLUTION: Find the equations of all the circles whose centers are on the line x=4 and that are tangent to the x axis and have a radius of 9 units.

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Question 293435: Find the equations of all the circles whose centers are on the line x=4 and that are tangent to the x axis and have a radius of 9 units.
Found 2 solutions by richwmiller, Edwin McCravy:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
(x-4)^2+(y-k)^2=81
where k=+9 and k=-9
Thanks to Ed for the correction.

Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
 

The other tutor only gave you one circle's equation.  There are two.

Draw the line x=4 which is a vertical line through 4 on the x-axis: 


The center has to be 9 units either above or below the x-axis
in order that the circle be tangent to the x-axis.  So we mark
these points.  They are the points (4,9) and (4,-9)



So we draw in the two circles:



Using the standard form of the equation of a circle:

%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2

For the top circle the center is (4,9) and the radius is 9, so
its equation is

%28x-4%29%5E2%2B%28y-9%29%5E2=9%5E2

For the bottom circle the center is (4,-9) and the radius is 9, so
its equation is

%28x-4%29%5E2%2B%28y%2B9%29%5E2=9%5E2

Edwin