# Thread: Equation of a circle

1. ## Equation of a circle

An airport is located at D(0,0) A plane is positioned at C(-9,-16). The radar at the airport covers the area xsquared+ysquared=324. Will the plane show up on the radar at its current position. Explain. I know it wont i just dont know how to mathematically justify that.

2. Originally Posted by euclid2
An airport is located at D(0,0) A plane is positioned at C(-9,-16). The radar at the airport covers the area xsquared+ysquared=324. Will the plane show up on the radar at its current position. Explain. I know it wont i just dont know how to mathematically justify that.
Translated mathematically, "Will the point C be inside the circle $x^2 + y^2 = 324$?"

Translated (co-ordinate)geometrically "Is $x=-9, y=-16$ such that $x^2 + y^2 \leq 324$?"

Now can you solve it?

3. Originally Posted by euclid2
An airport is located at D(0,0) A plane is positioned at C(-9,-16). The radar at the airport covers the area xsquared+ysquared=324. Will the plane show up on the radar at its current position. Explain. I know it wont i just dont know how to mathematically justify that.
Is $(-9,\,-16)$ a solution to the inequality $x^2 + y^2\le324?$ If so, the plane will show up on the radar. Otherwise it will not.

Here is another method: the radar covers an area of radius $\sqrt{324} = 18$. So find the distance between the origin and the point $(-9,\,-16)$ and see if it is less than, equal to, or greater than 18.

4. If i plug the numbers in it becomes 337=324, therefore since it is greater on the left side it will not the seen in the radar. Is this all the work necessary to show?

5. Originally Posted by euclid2
If i plug the numbers in it becomes 337=324, therefore since it is greater on the left side it will not the seen in the radar. Is this all the work necessary to show?
Yes.

$(-9)^2 + (-16)^2\le324\Rightarrow337\le324$ which is false, so the point does not satisfy the inequality.

6. Originally Posted by euclid2
If i plug the numbers in it becomes 337=324, therefore since it is greater on the left side it will not the seen in the radar. Is this all the work necessary to show?
Yes its enough and I think thats what is expected. However note that Reckoner's alternate solution is very elegant and mathematically justified