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Write the equation of a circle that has center (2,4) and passing through (4,1)
 one year ago
 one year ago
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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timo86mBest ResponseYou've already chosen the best response.1
r^2=(x2)^2+(y(4))^2 hold on i'll find r
 one year ago

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

timo86mBest ResponseYou've already chosen the best response.1
Use 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
 one year ago

colorfulBest ResponseYou've already chosen the best response.0
oh no wait I remember...
 one year ago

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

timo86mBest ResponseYou've already chosen the best response.1
more info http://www.regentsprep.org/Regents/math/algtrig/ATC1/circlelesson.htm
 one year ago

wildjay8Best ResponseYou've already chosen the best response.0
there is no more info
 one year ago

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

timo86mBest ResponseYou've already chosen the best response.1
Use 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
 one year ago

colorfulBest ResponseYou've already chosen the best response.0
well they tell you the center of the circle, so we know h and k
 one year ago

wildjay8Best ResponseYou've already chosen the best response.0
yes colorful you have it a little mixed around (xh)^2+(yk)^2=r^2
 one year ago

colorfulBest ResponseYou've already chosen the best response.0
well 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
 one year ago

colorfulBest ResponseYou've already chosen the best response.0
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

wildjay8Best ResponseYou've already chosen the best response.0
yes now i just have to write the equation
 one year ago

wildjay8Best ResponseYou've already chosen the best response.0
i think we use d formula
 one year ago

colorfulBest ResponseYou've already chosen the best response.0
well 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
 one year ago

wildjay8Best ResponseYou've already chosen the best response.0
radius would be 5 i think
 one year ago

colorfulBest ResponseYou've already chosen the best response.0
we still gotta find r though is it 5 ? let me check...
 one year ago

wildjay8Best ResponseYou've already chosen the best response.0
so final answer (x2)^2+(y+4)=5
 one year ago

wildjay8Best ResponseYou've already chosen the best response.0
think thaty is right does that 4 become positive on the y
 one year ago

colorfulBest ResponseYou've already chosen the best response.0
dw:1337146127268:dwI don't think the radius is 5 why do you think it's 5 ???
 one year ago

wildjay8Best ResponseYou've already chosen the best response.0
d=square root of 42 +1(4) square root of 2+3 Square root of 5
 one year ago

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

wildjay8Best ResponseYou've already chosen the best response.0
im coming up with (x2)^2+(y+4)^2=5 will someone verify or tell me where im wrong
 one year ago

wildjay8Best ResponseYou've already chosen the best response.0
good thinking colorful i did that before
 one year ago

colorfulBest ResponseYou've already chosen the best response.0
but it doesn't give 5...
 one year ago

wildjay8Best ResponseYou've already chosen the best response.0
which in my notes we had sqrt 18 we put radius as 18
 one year ago

colorfulBest ResponseYou've already chosen the best response.0
um... don't know what to tell you about that, sorry :(
 one year ago

colorfulBest ResponseYou've already chosen the best response.0
maybe there's a typo, or you copied something wrong?
 one year ago

wildjay8Best ResponseYou've already chosen the best response.0
so answer would be (x2)^2+(y+4)^2=13
 one year ago

wildjay8Best ResponseYou've already chosen the best response.0
thank you colorful for helping and pointing out mistake
 one year ago

colorfulBest ResponseYou've already chosen the best response.0
no problem :D welcome!
 one year ago

robtobeyBest ResponseYou've already chosen the best response.0
A Mathematica version of the solution with comments and a plot is attached.
 one year ago
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