Video transcript
– [ Voiceover ] So we have a traffic circle here and they specified some points for us. This little orangeish, or, I guess, maroonish-red point justly over here is the center of the circle, and then this blasphemous point is a charge that happens to sit on the circle. And therefore with that information, I want you to pause the television and see if you can figure out the equation for this lap. Alright, let ‘s work through this together. So get ‘s first think about the center of the circle. And the center of the circle is barely going to be the coordinates of that point. therefore, the x-coordinate is negative one and then the y-coordinate is one. therefore center is negative one comma one. And now, let ‘s think about what the spoke of the set is. well, the spoke is going to be the distance between the center and any point on the circle. thus, for exemplar, for example, this distance. The distance of that note. Let ‘s see I can do it thicker. A thick interpretation of that. This line, right over there. Something strange about my … Something foreign about my penitentiary tool. It ‘s making that very sparse. Let me do it one more clock. Okay, that ‘s better. ( laughs ) The distance of that line justly over there, that is going to be the radius. So how can we figure that out ? well, we can set up a right triangle and basically use the distance convention which comes from the Pythagorean Theorem. To figure out the duration of that occupation, so this is the radius, we could figure out a switch in adam. so, if we look at our change in ten right over here. Our change in ten as we go from the center to this point. So this is our change in adam. And then we could say that this is our change in y. That right over there is our change in y. And so our exchange in x-squared plus our switch in y-squared is going to be our spoke squared. That comes straight out of the Pythagorean Theorem. This is a right triangulum. And so we can say that r-squared is going to be equal to our change in x-squared plus our change in y-squared. Plus our change in y-squared. now, what is our deepen in x-squared ? Or, what is our change in ten going to be ? Our change in ten is going to be peer to, well, when we go from the radius to this item over here, our adam goes from negative one to six. So you can view it as our ending adam minus our starting ten. so negative one minus negative, blue, six minus negative one is equal to seven. therefore, let me … so, we have our deepen in ten, this correct over here, is equal to seven. If we viewed this as the beginning indicate and this as the goal detail, it would be negative seven, but we very care about the absolute value in the change of adam, and once you square it it all becomes a positive anyhow. So our change in ten right over here is going to be positive seven. And our change in yttrium, well, we are starting at, we are starting at y is equal to one and we are going to y is adequate to negative four. So it would be negative four minus one which is equal to negative five. And so our change in yttrium is damaging five. You can view this distance veracious all over hera as the absolute measure of our change in y, which of run would be the absolute value of five. But once you square it, it does n’t matter. The negative sign goes away. And then, this is going to simplify to seven squared, change in x-squared, is 49. change in y-squared, negative five squared, is 25. So we get r-squared, we get r-squared is peer to 49 plus 25. So what ‘s 49 plus 25 ? Let ‘s see, that ‘s going to be 54, or was it 74. r-squared is equal to 74. Did I do that right ? Yep, 74. And so now we can write the equation for the encircle. The circle is going to be all of the points that are, good, in fact, let me right all of the, so if r-squared is equal to 74, r is peer to the square-root of 74. And thus the equation of the encircle is going to be all points x comma y that are this far aside from the center. And indeed what are those points going to be ? Well, the distance is going to be adam minus the x-coordinate of the center. x minus negative one squared. Let me do that in a blue color. Minus negative one squared. Plus yttrium minus, y minus the y-coordinate of the plaza. y minus one squared. Squared. Is peer, is going to be peer to r-squared. Is going to be equal to the length of the spoke squared. Well, r-squared we already know is going to be 74. 74. And then if we want to simplify it a little bit, you subtract a negative, this becomes a incontrovertible. So it simplifies to x plus one square plus yttrium minus one squared is adequate to 74. Is equal to 74. And, we are all done.
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