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

- anonymous

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

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- anonymous

r^2=(x-2)^2+(y-(-4))^2
hold on i'll find r

- anonymous

why is it not\[r^2=(x+4)^2+(y-2)^2\]?

- 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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## More answers

- anonymous

oh no wait I remember...

- anonymous

the formula for a circle with center (h,k) is
r^2=(y-k)^2+(x-h)^2

- anonymous

more info
http://www.regentsprep.org/Regents/math/algtrig/ATC1/circlelesson.htm

- anonymous

there is no more info

- anonymous

yeah, but those links always confuse me
and then how do you find r again, isn't there some easy way?

- anonymous

- anonymous

well they tell you the center of the circle, so we know h and k

- anonymous

yes colorful you have it a little mixed around (x-h)^2+(y-k)^2=r^2

- 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

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

yes now i just have to write the equation

- anonymous

i think we use d formula

- 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

radius would be 5 i think

- anonymous

we still gotta find r though
is it 5 ?
let me check...

- anonymous

so final answer (x-2)^2+(y+4)=5

- anonymous

think thaty is right does that 4 become positive on the y

- anonymous

|dw:1337146127268:dw|I don't think the radius is 5
why do you think it's 5 ???

- anonymous

d=square root of 4-2 +-1-(-4) square root of 2+3 Square root of 5

- anonymous

\[d=\sqrt{(4-2)^2+(-1-(-4))^2}=\sqrt{2^2+3^2}\]

- anonymous

im coming up with (x-2)^2+(y+4)^2=5 will someone verify or tell me where im wrong

- anonymous

good thinking colorful i did that before

- anonymous

but it doesn't give 5...

- anonymous

radius is 13

- anonymous

sqrt(13)

- anonymous

which in my notes we had sqrt 18 we put radius as 18

- anonymous

um... don't know what to tell you about that, sorry :(

- anonymous

maybe there's a typo, or you copied something wrong?

- anonymous

so answer would be (x-2)^2+(y+4)^2=13

- anonymous

yeah, looks like it

- anonymous

thank you colorful for helping and pointing out mistake

- anonymous

no problem :D
welcome!

- anonymous

A Mathematica version of the solution with comments and a plot is attached.

##### 1 Attachment

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