What is the standard form of the equation of the circle?

Question

The figure to the right indicates that a university is located 3.2 miles west and 3.6 miles south of the center of the city. A seismograph on the campus shows that a small earthquake occurred.The quake's epicenter is estimated to be approximately 29 miles from the university.

 

 

Answer 1

There is no figure for a tutor to examine.  It is not clear what you are asking for, but it looks like you want a circle centered at the university, of radius equal to the distance from the university to the epicenter.  With the origin of coordinates at the center of the city, the coordinates of the university are

 

h = -3.2

k = -3.6

 

r = 29

 

Then the earthquake occurred inside the circle given by

 

(x - h)² + (y - k)² = r²

 

(x + 3.2)² + (y + 3.6)² = 29²