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wildjay8
 3 years ago
Write the equation of a circle that has center (2,4) and passing through (4,1)
wildjay8
 3 years ago
Write the equation of a circle that has center (2,4) and passing through (4,1)

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timo86m
 3 years ago
Best ResponseYou've already chosen the best response.1r^2=(x2)^2+(y(4))^2 hold on i'll find r

colorful
 3 years ago
Best ResponseYou've already chosen the best response.0why is it not\[r^2=(x+4)^2+(y2)^2\]?

timo86m
 3 years ago
Best ResponseYou've already chosen the best response.1Use distance formula to find r sqrt((delta x)^2+(delta y)^2) delta x just means difference in x which is xfxi = 42 Same for delta y

colorful
 3 years ago
Best ResponseYou've already chosen the best response.0oh no wait I remember...

colorful
 3 years ago
Best ResponseYou've already chosen the best response.0the formula for a circle with center (h,k) is r^2=(yk)^2+(xh)^2

timo86m
 3 years ago
Best ResponseYou've already chosen the best response.1more info http://www.regentsprep.org/Regents/math/algtrig/ATC1/circlelesson.htm

colorful
 3 years ago
Best ResponseYou've already chosen the best response.0yeah, but those links always confuse me and then how do you find r again, isn't there some easy way?

timo86m
 3 years ago
Best ResponseYou've already chosen the best response.1Use distance formula to find r sqrt((delta x)^2+(delta y)^2) delta x just means difference in x which is xfxi = 42 Same for delta y

colorful
 3 years ago
Best ResponseYou've already chosen the best response.0well they tell you the center of the circle, so we know h and k

wildjay8
 3 years ago
Best ResponseYou've already chosen the best response.0yes colorful you have it a little mixed around (xh)^2+(yk)^2=r^2

colorful
 3 years ago
Best ResponseYou've already chosen the best response.0well whether you write (xh)^2+(yk)^2=r^2 or (yk)^2+(xh)^2=r^2 it's the same thing, isn't it? and the picture should be something like this dw:1337145806387:dw

colorful
 3 years ago
Best ResponseYou've already chosen the best response.0so we want the radius r, and I think we can use the pythagorean formula from geometry to figure out how long it is...

wildjay8
 3 years ago
Best ResponseYou've already chosen the best response.0yes now i just have to write the equation

wildjay8
 3 years ago
Best ResponseYou've already chosen the best response.0i think we use d formula

colorful
 3 years ago
Best ResponseYou've already chosen the best response.0well you only need to find r now we already know the rest just plug in the numbers for h and k into (xh)^2+(yk)^2=r^2

wildjay8
 3 years ago
Best ResponseYou've already chosen the best response.0radius would be 5 i think

colorful
 3 years ago
Best ResponseYou've already chosen the best response.0we still gotta find r though is it 5 ? let me check...

wildjay8
 3 years ago
Best ResponseYou've already chosen the best response.0so final answer (x2)^2+(y+4)=5

wildjay8
 3 years ago
Best ResponseYou've already chosen the best response.0think thaty is right does that 4 become positive on the y

colorful
 3 years ago
Best ResponseYou've already chosen the best response.0dw:1337146127268:dwI don't think the radius is 5 why do you think it's 5 ???

wildjay8
 3 years ago
Best ResponseYou've already chosen the best response.0d=square root of 42 +1(4) square root of 2+3 Square root of 5

colorful
 3 years ago
Best ResponseYou've already chosen the best response.0\[d=\sqrt{(42)^2+(1(4))^2}=\sqrt{2^2+3^2}\]

wildjay8
 3 years ago
Best ResponseYou've already chosen the best response.0im coming up with (x2)^2+(y+4)^2=5 will someone verify or tell me where im wrong

wildjay8
 3 years ago
Best ResponseYou've already chosen the best response.0good thinking colorful i did that before

colorful
 3 years ago
Best ResponseYou've already chosen the best response.0but it doesn't give 5...

wildjay8
 3 years ago
Best ResponseYou've already chosen the best response.0which in my notes we had sqrt 18 we put radius as 18

colorful
 3 years ago
Best ResponseYou've already chosen the best response.0um... don't know what to tell you about that, sorry :(

colorful
 3 years ago
Best ResponseYou've already chosen the best response.0maybe there's a typo, or you copied something wrong?

wildjay8
 3 years ago
Best ResponseYou've already chosen the best response.0so answer would be (x2)^2+(y+4)^2=13

wildjay8
 3 years ago
Best ResponseYou've already chosen the best response.0thank you colorful for helping and pointing out mistake

colorful
 3 years ago
Best ResponseYou've already chosen the best response.0no problem :D welcome!

robtobey
 3 years ago
Best ResponseYou've already chosen the best response.0A Mathematica version of the solution with comments and a plot is attached.
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