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a circle in the XY plane has its centered 7 comma 14 if the point 7 comma 34 lies on the circle which of the following is an equation of the circle so let's just remind ourselves the general form of the equation of a circle if any of this looks like looks looks unusual to you you haven't seen it before I encourage you to watch the equation of a circle videos on Khan Academy but 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 and 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 then not circular I think you get the point so the radiuses are the 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 in K is H is 7 and K is 14 and we just need to figure out the radius if we figure that out we will be able to figure out the equation of the entire circle now they tell us that the center is at 7 comma 14 so that point right over there is 7 comma 14 and then the point 7 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 7 comma 34 it would be right above it we've just increased our Y without changing our X so 7 comma 14 is the center this point right over here 7 comma 34 lies on the circle so the circle is gonna look gonna look something something like this and so the the radius of this circle what we have to figure out is just the distance between these two points and 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 7 k is equal to 14 and r is equal to 20 so it's gonna be X minus H X minus 7 squared plus y minus K Y minus 14 squared is equal to is equal to R squared 20 squared is 400 and so let's see that is and that is this choice right over here X minus 7 squared plus y minus 14 squared is equal to 400 and we're done