Question

Radio waves

KROC radio station is 4miles west and 6 miles north of center bigcity. KROC can only be heard clearly 5.5 miles from the station.write and equation for the boundry where the radio station can clearly be heard.

Answer 1

Consider cartesian coordinate system with origin at the big city in 2-dimensions.

West indicates the negative x axis, east indicates positive x axis.

North indicates Positive y axis, south indicates negative y axis.

KROC radio station is situated at position (xc,yc) = (-4,6). Since it is located 4 miles west and 6 miles north.

The radio station can be heard clearly upto a distance of 5.5miles. Which is infact a circle of radius 5.5miles upto which the radio station can be heard clearly.

This circle will have the center at the position of the radio station.

The circle upto which the radio station can be heard clearly has center at (-4,6) and radius 5.5miles.

The equation of circle is :

(x - xc)^2 + (y - yc)^2 = 5.5^2

(x + 4)^2 + (y - 6)^2 = 5.5*5.5 = 30.25

(x + 4)^2 + (y - 6)^2 = 30.25

is the equation upto which the radio station can be heard clearly.

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