An electronic toy car only travels along the line 10x-40y=200. A wireless charging station is located at (50,50) and a toy car can be recharged at a distance of 40 units.

Question

1. at what point is the car closest to the station?
2. at this point, how far is it to the station? will it be charged?

Answer 1

the distance z from any point (x,y) to (50,50) is z = √((50-x)^2 + (50-y)^2)
Since y = (10x+200)/40,
So, z = √((50-x)^2 + (50-(10x+200)/40)^2)

Now just find where dz/dx=0
and yes, it will get charged.