anonymous
  • anonymous
Write the equation of a circle that has center (2,-4) and passing through (4,-1)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
r^2=(x-2)^2+(y-(-4))^2 hold on i'll find r
anonymous
  • anonymous
why is it not\[r^2=(x+4)^2+(y-2)^2\]?
anonymous
  • anonymous
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

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anonymous
  • anonymous
oh no wait I remember...
anonymous
  • anonymous
the formula for a circle with center (h,k) is r^2=(y-k)^2+(x-h)^2
anonymous
  • anonymous
more info http://www.regentsprep.org/Regents/math/algtrig/ATC1/circlelesson.htm
anonymous
  • anonymous
there is no more info
anonymous
  • anonymous
yeah, but those links always confuse me and then how do you find r again, isn't there some easy way?
anonymous
  • anonymous
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
anonymous
  • anonymous
well they tell you the center of the circle, so we know h and k
anonymous
  • anonymous
yes colorful you have it a little mixed around (x-h)^2+(y-k)^2=r^2
anonymous
  • anonymous
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|
anonymous
  • anonymous
so we want the radius r, and I think we can use the pythagorean formula from geometry to figure out how long it is...
anonymous
  • anonymous
yes now i just have to write the equation
anonymous
  • anonymous
i think we use d formula
anonymous
  • anonymous
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
anonymous
  • anonymous
radius would be 5 i think
anonymous
  • anonymous
we still gotta find r though is it 5 ? let me check...
anonymous
  • anonymous
so final answer (x-2)^2+(y+4)=5
anonymous
  • anonymous
think thaty is right does that 4 become positive on the y
anonymous
  • anonymous
|dw:1337146127268:dw|I don't think the radius is 5 why do you think it's 5 ???
anonymous
  • anonymous
d=square root of 4-2 +-1-(-4) square root of 2+3 Square root of 5
anonymous
  • anonymous
\[d=\sqrt{(4-2)^2+(-1-(-4))^2}=\sqrt{2^2+3^2}\]
anonymous
  • anonymous
im coming up with (x-2)^2+(y+4)^2=5 will someone verify or tell me where im wrong
anonymous
  • anonymous
good thinking colorful i did that before
anonymous
  • anonymous
but it doesn't give 5...
anonymous
  • anonymous
radius is 13
anonymous
  • anonymous
sqrt(13)
anonymous
  • anonymous
which in my notes we had sqrt 18 we put radius as 18
anonymous
  • anonymous
um... don't know what to tell you about that, sorry :(
anonymous
  • anonymous
maybe there's a typo, or you copied something wrong?
anonymous
  • anonymous
so answer would be (x-2)^2+(y+4)^2=13
anonymous
  • anonymous
yeah, looks like it
anonymous
  • anonymous
thank you colorful for helping and pointing out mistake
anonymous
  • anonymous
no problem :D welcome!
anonymous
  • anonymous
A Mathematica version of the solution with comments and a plot is attached.
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