Question

The geographic center of Tennessee is near Murfreesboro. The closest Doppler weather radar is in Nashville. If Murfreesboro is designated as the origin, then Nashville has coordinates (–58, 55), where each unit is one mile. If the radar has a radius of 80 miles, write an equation for the circle that represents radar coverage from Nashville.

Answer 1

1) Nashville = center = (-58, 55) => Xc = - 58miles, Yc = 55miles

2) radius = 8 miles

3) General equation of a circle: (x - Xc)^2 + (y - Yc)^2 = radius^2

4) equation of the circle that represents radar coveraga:

(x - (-58) )^2 + (y - 55)^2 = 80^2

=> (x + 58)^2 + (y - 55)^2 = 6400

Answer: (x + 58)^2 + (y - 55)^2 = 6400