Before watching the video didn’t know anything about the equations of circles. The only thing that I knew was what a circle was.
After watching the video I learned about the standard form of a circle. It is x minus h to the second plus y minus k to the second equals r to the second. H and K is the center of the circle and r is the radius of the circle. So, you can use this in order to find the radius of the circle. For example, if the center is five and negative one and there is a point on the circle that is one, two, you can plug that into the equation r equals the square root of x-h to the second plus y minus k to the second and get you radius. So, after you add and subtract your information after plugging it in, you get the radius to equal the square root of negative four to the second plus three to the second. After you square the numbers you get r to equal the square root of sixteen plus nine, or the square root of twenty-five. The square root of twenty-five is five, so your radius equals five. Lastly you plug that into the standard form and get your equation to be x minus five to the second plus y minus one to the second equation five to the second, or twenty-five. You can also graph the equation onto a graph, so basically you are doing the opposite; you are given the equation and you have to graph it. This is everything that I learned about after watching the video.
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Questions:
For your second question you need to look at all of the possible graphs given to you. When you look at your equation you have...x squared + (y-5)=25. When you simplify out your equation you have x squared plus y (5)^2. When you take negative 5 times your squared you are going to get 25. When you look at your graphs the only answer that would make sense is letter B.
ReplyDeleteFor your first question we know that the center for x is at 0 and y is 3. We know that another point is (0,6) so we have to find the distance. We count three units which is the radius. The radius squared is 9 then. We then can put our information we have into standard form remembering that we have to put it in the positive forms so it makes sense and gives us the correct equation. So standard form is: 9= x squared + y - 3 squared. The equation then has to be answer D!
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