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Current time:0:00Total duration:3:50

Features of a circle from its graph

CCSS.Math:

Video transcript

so we have a circle right over here and the first question we'll ask ourselves is what are the coordinates of the center of that circle well we can eyeball that we can see look it looks like the center it looks like the circle is centered on that point right over there and the coordinates of that point the x-coordinate is negative 4 and the y-coordinate is negative 7 so the center of that circle would be the point negative 4 comma negative 7 now let's say on top of that someone were to tell us someone were to tell us that this point negative 5 comma negative 9 is also on the circle so negative 5 comma negative 9 on is on the circle so based on this information the coordinate of the center and a point that sits on the circle can we figure out the radius well the radius is just the distance between the center of the circle and any point on the circle in fact one of the most typical definitions of a circle is all of the points that are the same distance or that are the radius away from from another point from the second and that other point would be the center of the circle so how do we find out the distance between between these two points between these two points so the length of that orange line well we can use the distance formula which is essentially the Pythagorean theorem the distance squared so if this is the length of that is the distance so we could say the distance squared is going to be equal to is going to be equal to our change in x squared so that right there is our change in X and not to write really small but that's our change in X our change in x squared plus our change in Y squared our change in Y squared change in Y squared now what is our change in X our change in X and you can even eyeball it here it looks like it's 1 but let's verify it we could view this point as the it doesn't matter which one use views the start at the end as long as you're consistent so let's see if we view this as the the end we'd say negative five it'd be negative five minus negative four minus negative four and so this would be equal to negative one so when you go from the center to this outer point negative five comma nine negative five comma negative nine you go one back in the x-direction now the actual this distance would just be the absolute value of that but doesn't matter that this is a negative because we're about to square it and so that negative sign will go away now what is our change in Y our change in Y well this is the finishing y negative nine minus minus negative seven minus our initial y is equal to negative two and notice just go from that point that Y to that pot Y we go to negative two so actually we could call the length of that side as the absolute value of our change in Y and we can view this is the absolute value of our change in X and it doesn't really matter because once we square them the negatives go away so our distance squared our distance squared I really could call this the radius squared is going to be equal to our change in x squared well it's negative one squared which is just going to be one plus our change in Y squared negative two squared is just positive four one plus four and so you have your distance squared is equal to five or that the distance is equal to the square root of five and I could have just called this variable the radius so we could say the radius is equal to the square root of five and we're done