Using circles to find points

[Bogogogo]

I’m working on a problem where I need to find a point on the circle given the radius and the center. I tried using the distance formula with 4 as the distance, but got (square root) of 17 +4

 

[MarkFL]

I would begin by orienting the town's center at the origin, and giving the boundary of the cell tower's coverage as:

[MATH](x-4)^2+(y-5)^2=4^2[/MATH]
Now, the house must lie along the line \(y=6\) (the dashed line in the following diagram)



So, we need to find the places where this line intersects the circle, and take the one with the larger \(x\)-coordinate. Can you proceed?

 

[Bogogogo]

I would begin by orienting the town's center at the origin, and giving the boundary of the cell tower's coverage as:

[MATH](x-4)^2+(y-5)^2=4^2[/MATH]
Now, the house must lie along the line \(y=6\) (the dashed line in the following diagram)

View attachment 13520

So, we need to find the places where this line intersects the circle, and take the one with the larger \(x\)-coordinate. Can you proceed?

I am unsure. Would I use the Pythagorean equation to find the distance?

 

[MarkFL]

Well, we know that \(y=6\), so put that into the equation for the circle, and solve for \(x\), taking the larger root.

[MATH](x-4)^2+(6-5)^2=4^2[/MATH]
This will tell you directly how far east of the town center the house is located.