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

Answer:

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

Step-by-step 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

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