Question 609537
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Use the midpoint formulas to calculate the midpoint of the diameter, which is to say the center of the circle.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x_m\ = \frac{x_1 + x_2}{2}] and


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y_m\ = \frac{y_1 + y_2}{2}]


where *[tex \Large \left(x_1,y_1\right)] and *[tex \Large \left(x_2,y_2\right)] are the coordinates of the given diameter endpoints.


Use the distance formula to calculate the measure of the radius of the circle


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ d\ =\ sqrt{(x_1\ -\ x_2)^2\ +\ (y_1\ -\ y_2)^2}]


where *[tex \Large \left(x_1,y_1\right)] and *[tex \Large \left(x_2,y_2\right)] are the coordinates of either diameter endpoint and the calculated diameter midpoint.


Write the equation of the circle centered at *[tex \LARGE (h,k)] with radius *[tex \LARGE r]:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ (x\ -\ k)^2\ +\ (y\ -\ h)^\ =\ r^2]


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
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