Question

An airport is located at the point (-4, 3). The noise of planes landing and taking off can be heard up to 3 miles away. Write the inequality of a circle that represents the situation

Answer 1

The correct answer is:
`( x + 4) ^ {2} + (y - 3) ^ {2} \leq 9`

Explanation:

The airport is located at the point (-4 , 3). Thus we can consider the center of the circle to be this particular point.

Since the noise can be heard till 3 miles away, this implies we can consider the radius of the circle to be 3.

We all know the general equation of circle with center at (
`\alpha` ,
`\beta`) with radius r is given by:

`(x - \alpha ) ^(2) + (y - \beta )^(2) = r^(2)`

Here the value of
`\alpha` is (-4) ; value of
`\beta` is 3 ; and value of r is 3.

Now since the noise of landing and taking off of the planes would be within the circle, hence we use less than equal to (
`\leq`) sign instead of equal to sign.

Thus the general equation of noise of the planes can be given by the inequality

`( x - (- 4)) ^ {2} + (y - 3) ^ {2} \leq 3^(2)\\= ( x + 4) ^ {2} + (y - 3) ^ {2} \leq 3^(2)`