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

Mathematics
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r^2=(x-2)^2+(y-(-4))^2 hold on i'll find r
why is it not\[r^2=(x+4)^2+(y-2)^2\]?
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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Other answers:

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