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anonymous

  • one year ago

What is the equation of the following graph?

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  1. anonymous
    • one year ago
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  2. mathstudent55
    • one year ago
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    Equation of a circle with radius r, and center at (h, k). \((x - h)^2 + (y - k)^2 = r^2\)

  3. mathstudent55
    • one year ago
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    Start by finding two things: 1. What is the radius of the circle? 2. What are the coordinates of the center of the circle?

  4. mathstudent55
    • one year ago
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    @biddyB Are you there?

  5. anonymous
    • one year ago
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    Sorry I was actually wrong! mathstudent55 is right. Sorry for the confusion!

  6. anonymous
    • one year ago
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    Ok, whew, I was really confused for a second. Thats ok, I get it now, thanks

  7. anonymous
    • one year ago
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    How do I find the radius?

  8. mathstudent55
    • one year ago
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    First, find the center.

  9. anonymous
    • one year ago
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    0?

  10. mathstudent55
    • one year ago
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    |dw:1438645154737:dw|

  11. mathstudent55
    • one year ago
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    I think you got the right idea, but the center is actually (0, 0) since it's a point. It needs to have an x-coordinate and a y-coordinate.

  12. mathstudent55
    • one year ago
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    Now that you know where the center is, the radius is the distance from the center point to any point on the circle.

  13. mathstudent55
    • one year ago
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    It's easier if you measure along a horizontal or a vertical line.

  14. mathstudent55
    • one year ago
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    |dw:1438645313174:dw|

  15. anonymous
    • one year ago
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    3?

  16. mathstudent55
    • one year ago
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    Correct. The radius is 3. That means r = 3 The center of the circle is (0, 0). That means h = 0, and k = 0. Now we use these values in the equation above.

  17. mathstudent55
    • one year ago
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    \((x - h)^2 + (y - k)^2 = r^2\) \((x - 0)^2 + (y - 0)^2 = 3^2\) You see the substitutions of 0 for h, 0 for k, and 3 for r?

  18. mathstudent55
    • one year ago
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    Now we just simplify to: \(\large x^2 + y^2 = 9\) That is the answer.

  19. anonymous
    • one year ago
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    Thank you! that was really well explained, I get it

  20. anonymous
    • one year ago
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    For this one r=4? that seems too simple @mathstudent55

  21. anonymous
    • one year ago
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  22. mathstudent55
    • one year ago
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    Correct. For the second problem, r = 4. Now you need to coordinates of the center. What are they? Remember, you are looking for an ordered pair of the form (x, y) for the center.

  23. anonymous
    • one year ago
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    (3,5)?

  24. mathstudent55
    • one year ago
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    Correct. Now you let h = 3, k = 5, and r = 4, and you substitute these values in the equation of a circle.

  25. anonymous
    • one year ago
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    (x-3)^2 +(y-5)^2=4^2 ?

  26. mathstudent55
    • one year ago
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    Correct.

  27. anonymous
    • one year ago
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    That's it, it doesn't get simplified any more?

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