Question

A radio tower is centered at (6,-16) on a coordinate grid where each unit represents 1 mile the radio signals range is 80 miles write a standard equation that describes the position and range of the tower

Answer 1

`(x-6)^(2)+(y+16)^(2)=6,400`

Explanation:

we know that

The equation of a circle in standard form is equal to

`(x-h)^(2)+(y-k)^(2)=r^(2)`

In this problem we have

The center of the radio tower (position) is the point
`(6,-16)`

The radius of the radio tower (range) is
`r=80\ miles`

substitute

`(x-6)^(2)+(y+16)^(2)=80^(2)`

`(x-6)^(2)+(y+16)^(2)=6,400`