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Current time:0:00Total duration:2:49

Circle equations — Harder example

Video transcript

- [Instructor] A circle in the xy-plane has its center at seven comma 14. If the point seven comma 34 lies on the circle, which of the following is an equation of the circle? Let's just remind ourselves the general form of the equation of a circle. If any of this looks like, looks unusual to you, you haven't seen it before, I encourage you to watch the equation of a circle videos on Kahn Academy. The general form for the equation of a circle, if we have a circle that's centered at the point h comma k, the x-coordinate of the center is h. The y-coordinate of the center is k. If it has a radius of r, so the circle is gonna look something like that. I'm trying to draw it as circular as I can. Man, that's not so circular. I think you get the point. The radius is r. This equation, the equation of this circle, of all the points that are exactly r away from the point h comma k, is going to be x minus the x-coordinate of the center squared plus y minus the y-coordinate of the center squared is equal to the radius squared. Now in this case, we know what our h and k is. H is seven, and k is 14, and we just need to figure out the radius. We figure that out, we will be able to figure out the equation of the entire circle. Now, they tell us that the center's at seven comma 14, so that point right over there is seven comma 14, and then the point seven comma 34 also lies on the circle, so it has the same x-coordinate. Its y-coordinate is just higher, so this might be, that right over there might be the point seven comma 34. It would be right above it. We just increased our y without changing our x. So, seven comma 14 is the center. This point right over here is seven comma 34, lies on the circle, so the circle is gonna look something like this, and so the radius of this circle, what we have to figure out, is just the distance between these two points. These two points, you don't even have to really apply the distance formula or anything like this. The distance here is just our change in y. Our x doesn't change. It's gonna be 34 minus 14. So, the radius here is equal to 20. So, now we know. We know h is equal to seven. K is equal to 14, and r is equal to 20. So, it's gonna be x minus h, x minus seven squared plus y minus k, y minus 14 squared is equal to r squared. 20 squared is 400. So let's see, that is this choice right over here. X minus seven squared plus y minus 14 squared is equal to 400, and we're done.