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.

Question

Mathematics

Commando

27 October, 05:11

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.

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Evelyn Stevens · 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