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wildjay8

  • 2 years ago

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

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

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

  3. timo86m
    • 2 years ago
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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

  4. colorful
    • 2 years ago
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    oh no wait I remember...

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

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

  7. wildjay8
    • 2 years ago
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    there is no more info

  8. colorful
    • 2 years ago
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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?

  9. timo86m
    • 2 years ago
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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

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

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

  12. colorful
    • 2 years ago
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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|

  13. colorful
    • 2 years ago
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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...

  14. wildjay8
    • 2 years ago
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    yes now i just have to write the equation

  15. wildjay8
    • 2 years ago
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    i think we use d formula

  16. colorful
    • 2 years ago
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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

  17. wildjay8
    • 2 years ago
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    radius would be 5 i think

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

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

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

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

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

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

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

  25. wildjay8
    • 2 years ago
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    good thinking colorful i did that before

  26. colorful
    • 2 years ago
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    but it doesn't give 5...

  27. wildjay8
    • 2 years ago
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    radius is 13

  28. colorful
    • 2 years ago
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    sqrt(13)

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

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

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

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

  33. colorful
    • 2 years ago
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    yeah, looks like it

  34. wildjay8
    • 2 years ago
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    thank you colorful for helping and pointing out mistake

  35. colorful
    • 2 years ago
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    no problem :D welcome!

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

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