Question

a rectangular coordinate system with coordinates in miles is placed with the origin at the center of a city. the figure to the right indicates that a university is located 3.5 miles west and 2.2 miles south of the center of the city. a seismograph on the campus shows that a small earthquake occurred. the quakes epicenter is estimated to be approximately 23 miles from the university. write the standard form of the equation for the set of points that could be the epicenter of the quake. what is the standard form of the equation of the circle?

Explanation:

Step1: Recall circle - equation formula

The standard form of the equation of a circle is $(x - h)^2+(y - k)^2=r^2$, where $(h,k)$ is the center of the circle and $r$ is the radius.

Step2: Identify center and radius

The university is at the point $(- 3.5,-2.2)$ which is the center of the circle $(h = - 3.5,k=-2.2)$, and the radius $r = 23$ (distance from the university to the possible epicenter).

Step3: Substitute values into formula

Substitute $h=-3.5$, $k = - 2.2$, and $r = 23$ into the standard - form equation: $(x+3.5)^2+(y + 2.2)^2=23^2$.

Answer:

$(x + 3.5)^2+(y+2.2)^2 = 529$