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# Graphing circles from features

CCSS.Math:

## Video transcript

we're asked to graph the circle which is centered at 3 comma negative 2 and has a radius of 5 units and I got this exercise off of the Khan Academy graph a circle according to its features exercise it's a pretty neat little widget here because what I can do is I can take this dot and I can move it around to redefine the center of the circle so it's centered at 3 comma negative 2 so X is 3 and Y is negative 2 so that's its center it has to have a radius of 5 the way it's drawn right now it has a radius of 1 the distance between the center and the actual circle the the points that define the circle right now it's 1 I need to make this radius equal to 5 so let's see if I take that so now the radius is equal to 2 3 4 & 5 there you go Center 2 3 comma negative 2 radius of 5 notice to go from the center to the actual circle it's 5 no matter where you go let's do one more of these graph the circle which is centered at negative 4 comma 1 and which has the point 0 comma 4 on it so once again let's drag the center so it's going to be negative 4 X is negative 4 y is 1 so that's the center it has the point 0 comma 4 on it so x is 0 Y is 4 so I have to drag I have to increase the radius of the circle let's see whoops nope I want to make sure I don't change the center I want to increase the radius of the circle until it includes this point right over here 0 comma 4 so I'm not there quite yet there you go I am now including the point 0 comma 4 and if we're curious what the radius is we could just go along the x axis x equals negative 4 is the x-coordinate for the center and we see that this point that this so this is negative 4 comma 1 and we see that 1 comma 1 is actually on the circle so the distance here is y 0 4 then another one it's 5 so this has a radius of 5 but either way we did what they asked us to do