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anonymous

  • one year ago

What is the equation of this circle in standard form? (x − 5.5)squared + (y − 4)squared = 7 (x + 5.5)squared + (y + 4)squared = 3.5 (x − 5.5)squared + (y − 4)squared = 3.5 (x + 5.5)squared + (y + 4)squared = 12.25 (x − 5.5)squared + (y − 4)squared = 12.25

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  1. anonymous
    • one year ago
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    |dw:1436206108326:dw|

  2. anonymous
    • one year ago
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    Is the center (2,4) and the point on the circle (9,4)?

  3. anonymous
    • one year ago
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    no, (2,4) is also a point on the circle

  4. anonymous
    • one year ago
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    the center doesn't have any coordinates

  5. anonymous
    • one year ago
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    Ok, that makes more sense. So |dw:1436206427235:dw|

  6. anonymous
    • one year ago
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    correct

  7. anonymous
    • one year ago
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    So the diameter would be 7, right?

  8. anonymous
    • one year ago
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    im not sure

  9. anonymous
    • one year ago
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    ohh wait yea, sorry i had a dumb moment

  10. anonymous
    • one year ago
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    Well, you can always fall back on the distance formula \[\large d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\]\[\large d=\sqrt{(9-2)^{2} + (4-4)^{2}}\]\[\large d=\sqrt{(7)^2}\]\[\large d=7\]

  11. anonymous
    • one year ago
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    But anyways, the diameter is 7, that means that the center of the circle is halfway between the x's of (2,4) and (9,4) right? Can you figure out what it is?

  12. anonymous
    • one year ago
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    3.5

  13. anonymous
    • one year ago
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    ?

  14. anonymous
    • one year ago
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    @LegendarySadist hey sorry! something happened that it logged me out

  15. anonymous
    • one year ago
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    Hey, I'm back. Openstudy update kicked me out too

  16. anonymous
    • one year ago
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    i got a little worried there lol i thought u weren't going to log back in

  17. anonymous
    • one year ago
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    Anyway, if we know the radius is 3.5, then just add 3.5 to 2 to get the x of the center point.

  18. anonymous
    • one year ago
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    5.5

  19. anonymous
    • one year ago
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    Right, and the y is the same as both points.

  20. anonymous
    • one year ago
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    So now we have all the info we need. All that's left is to put it into standard form. \[\large (x-h)^{2}~+~(y-k)^{2}=r^{2}\] \[\large (h,k)~=~Center~coordinates~of~circle\] \[\large r~=~radius\]

  21. anonymous
    • one year ago
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    i hate this part like what is k supposed to be!?

  22. anonymous
    • one year ago
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    \[\large (h,k) = (x,y)\\\large h=x \\\large k=y\]

  23. anonymous
    • one year ago
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    ok give me a sec

  24. anonymous
    • one year ago
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    wait but the y is what?

  25. anonymous
    • one year ago
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    (h,k) is the (x,y) of the center coordinates. The k is the y of the center.

  26. anonymous
    • one year ago
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    but what number does k stand for? lol im sorry

  27. anonymous
    • one year ago
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    It's the same y as the other 2 points, so 4.

  28. anonymous
    • one year ago
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    and x is 5.5?

  29. anonymous
    • one year ago
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    Yep

  30. anonymous
    • one year ago
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    i got 0

  31. anonymous
    • one year ago
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    wait is it A?

  32. anonymous
    • one year ago
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    Almost \[\large r^{2}\] not \[\large 2r\] So \[\large 3.5^{2}\]

  33. anonymous
    • one year ago
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    so it's either D or E

  34. anonymous
    • one year ago
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    is it E?

  35. anonymous
    • one year ago
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    Yes, it would be E.

  36. anonymous
    • one year ago
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    thank you sooo much!!!

  37. anonymous
    • one year ago
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    \[\huge \color{aqua}N\color{fuchsia}o \space \color{lime}P \color{orange}r \color{blue}o \color{maroon}b \color{red}l \color{olive}e \color{purple}m \ddot\smile \]

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