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wildjay8

Write the equation of a circle that has center (2,-4) and passing through (4,-1)

  • one year ago
  • one year ago

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  1. timo86m
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    r^2=(x-2)^2+(y-(-4))^2 hold on i'll find r

    • one year ago
  2. colorful
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    why is it not\[r^2=(x+4)^2+(y-2)^2\]?

    • one year ago
  3. timo86m
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    Use distance formula to find r sqrt((delta x)^2+(delta y)^2) delta x just means difference in x which is xf-xi = 4-2 Same for delta y

    • one year ago
  4. colorful
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    oh no wait I remember...

    • one year ago
  5. colorful
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    the formula for a circle with center (h,k) is r^2=(y-k)^2+(x-h)^2

    • one year ago
  6. timo86m
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    more info http://www.regentsprep.org/Regents/math/algtrig/ATC1/circlelesson.htm

    • one year ago
  7. wildjay8
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    there is no more info

    • one year ago
  8. colorful
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    yeah, but those links always confuse me and then how do you find r again, isn't there some easy way?

    • one year ago
  9. timo86m
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    Use distance formula to find r sqrt((delta x)^2+(delta y)^2) delta x just means difference in x which is xf-xi = 4-2 Same for delta y

    • one year ago
  10. colorful
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    well they tell you the center of the circle, so we know h and k

    • one year ago
  11. wildjay8
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    yes colorful you have it a little mixed around (x-h)^2+(y-k)^2=r^2

    • one year ago
  12. colorful
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    well whether you write (x-h)^2+(y-k)^2=r^2 or (y-k)^2+(x-h)^2=r^2 it's the same thing, isn't it? and the picture should be something like this |dw:1337145806387:dw|

    • one year ago
  13. colorful
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    so we want the radius r, and I think we can use the pythagorean formula from geometry to figure out how long it is...

    • one year ago
  14. wildjay8
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    yes now i just have to write the equation

    • one year ago
  15. wildjay8
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    i think we use d formula

    • one year ago
  16. colorful
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    well you only need to find r now we already know the rest just plug in the numbers for h and k into (x-h)^2+(y-k)^2=r^2

    • one year ago
  17. wildjay8
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    radius would be 5 i think

    • one year ago
  18. colorful
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    we still gotta find r though is it 5 ? let me check...

    • one year ago
  19. wildjay8
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    so final answer (x-2)^2+(y+4)=5

    • one year ago
  20. wildjay8
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    think thaty is right does that 4 become positive on the y

    • one year ago
  21. colorful
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    |dw:1337146127268:dw|I don't think the radius is 5 why do you think it's 5 ???

    • one year ago
  22. wildjay8
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    d=square root of 4-2 +-1-(-4) square root of 2+3 Square root of 5

    • one year ago
  23. colorful
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    \[d=\sqrt{(4-2)^2+(-1-(-4))^2}=\sqrt{2^2+3^2}\]

    • one year ago
  24. wildjay8
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    im coming up with (x-2)^2+(y+4)^2=5 will someone verify or tell me where im wrong

    • one year ago
  25. wildjay8
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    good thinking colorful i did that before

    • one year ago
  26. colorful
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    but it doesn't give 5...

    • one year ago
  27. wildjay8
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    radius is 13

    • one year ago
  28. colorful
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    sqrt(13)

    • one year ago
  29. wildjay8
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    which in my notes we had sqrt 18 we put radius as 18

    • one year ago
  30. colorful
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    um... don't know what to tell you about that, sorry :(

    • one year ago
  31. colorful
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    maybe there's a typo, or you copied something wrong?

    • one year ago
  32. wildjay8
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    so answer would be (x-2)^2+(y+4)^2=13

    • one year ago
  33. colorful
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    yeah, looks like it

    • one year ago
  34. wildjay8
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    thank you colorful for helping and pointing out mistake

    • one year ago
  35. colorful
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    no problem :D welcome!

    • one year ago
  36. robtobey
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    A Mathematica version of the solution with comments and a plot is attached.

    • one year ago
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