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Circle equations — Basic example

Watch Sal work through a basic Circle equations problem.

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Video transcript

- [Instructor] A circle in the xy-plane has a diameter with endpoints at eight comma 10, and negative two comma zero. Which of the following is the center of the circle? So let's think about it. If you have some circle in the xy-plane, so this is my best attempt at drawing a circle, and if you had two endpoints of a diameter, so let's say that this is a diameter right over here. And it looks something like this. So let's say that's our diameter right over there, and if this point was the point negative two comma zero and this was the point eight comma 10, what would be the coordinates of the center of the circle? Well the coordinates of the center of the circle is going to be the midpoint of these two endpoints of a diameter. In fact, the center of a circle is always going to be the midpoint of the two endpoints of the center of a diameter. If the diameter was this right over here, if the diameter was this over here, then once again the center of the circle is the midpoint of that point and that point right over there. So to answer this question we just have to find the midpoint of this point and this point right over there. And to find a midpoint we just have to find the average of the x-coordinates and the average of the y-coordinates. So let's see, this is gonna be eight, the x-coordinate. The average of eight and negative two is eight plus negative two over two. And the average of 10 and zero, we know that's five, but we could say that's 10 plus zero over two. Now let's see. Eight plus negative two is six, divided by two is three. And then ten divided by two is five. Three comma five. And we see it right over there.