00:01
Circles and their equations have many different applications to real life situations.
00:05
So for example, if we are studying an earthquake and we know that its epicenter is at a certain point and that there is a radius of affected areas where the earthquake could be felt, and we want to know whether a person living at x coordinate is inside or outside of the radius of where the earthquake can be felt.
00:26
So take for example, if we know that our epicenter or the center of our circle is at the point 37 and that an earthquake has a radius of 12, so 12 miles in any direction this earthquake was felt, we want to know if a person living at a certain point, say at a coordinate 13 -1, felt the earthquake.
00:51
So to know whether or not a person living at this coordinate about the earthquake, we first need to write an equation of our circle that represents or that models this particular earthquake.
01:07
So to do that, we know that the standard form of a circle is x minus h squared plus y minus k squared equals r squared, where the point hk is the center and r is the radius so we know our center point which is 3 -7 so we know that our equation is x minus 3 squared plus y minus 7 squared equals and we know our radius r is 12 so 12 squared is 144 so this is the equation of the circle that models this particular earthquake.
01:56
So what about this person living over here at the coordinates 13 -1? did they feel the earthquake? so one way to find that out is measuring the distance between the epicenter 3 -7 and this person 13 -1.
02:13
So our distance formula is d equals the square root of x2 minus x1 squared plus y -2 minus y -1 squared squared.
02:27
So looking at our two points, d equals square root x2 would be 13 minus x1, 3, all squared, plus y2, which would be 1, and y1, which is 7 squared...