wildjay8
Write the equation of a circle that has center (2,-4) and passing through (4,-1)
Delete
Share
This Question is Closed
timo86m
Best Response
You've already chosen the best response.
1
r^2=(x-2)^2+(y-(-4))^2
hold on i'll find r
colorful
Best Response
You've already chosen the best response.
0
why is it not\[r^2=(x+4)^2+(y-2)^2\]?
timo86m
Best Response
You'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 xf-xi = 4-2
Same for delta y
colorful
Best Response
You've already chosen the best response.
0
oh no wait I remember...
colorful
Best Response
You've already chosen the best response.
0
the formula for a circle with center (h,k) is
r^2=(y-k)^2+(x-h)^2
wildjay8
Best Response
You've already chosen the best response.
0
there is no more info
colorful
Best Response
You'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?
timo86m
Best Response
You'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 xf-xi = 4-2
Same for delta y
colorful
Best Response
You've already chosen the best response.
0
well they tell you the center of the circle, so we know h and k
wildjay8
Best Response
You've already chosen the best response.
0
yes colorful you have it a little mixed around (x-h)^2+(y-k)^2=r^2
colorful
Best Response
You've already chosen the best response.
0
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|
colorful
Best Response
You'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...
wildjay8
Best Response
You've already chosen the best response.
0
yes now i just have to write the equation
wildjay8
Best Response
You've already chosen the best response.
0
i think we use d formula
colorful
Best Response
You'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 (x-h)^2+(y-k)^2=r^2
wildjay8
Best Response
You've already chosen the best response.
0
radius would be 5 i think
colorful
Best Response
You've already chosen the best response.
0
we still gotta find r though
is it 5 ?
let me check...
wildjay8
Best Response
You've already chosen the best response.
0
so final answer (x-2)^2+(y+4)=5
wildjay8
Best Response
You've already chosen the best response.
0
think thaty is right does that 4 become positive on the y
colorful
Best Response
You've already chosen the best response.
0
|dw:1337146127268:dw|I don't think the radius is 5
why do you think it's 5 ???
wildjay8
Best Response
You've already chosen the best response.
0
d=square root of 4-2 +-1-(-4) square root of 2+3 Square root of 5
colorful
Best Response
You've already chosen the best response.
0
\[d=\sqrt{(4-2)^2+(-1-(-4))^2}=\sqrt{2^2+3^2}\]
wildjay8
Best Response
You've already chosen the best response.
0
im coming up with (x-2)^2+(y+4)^2=5 will someone verify or tell me where im wrong
wildjay8
Best Response
You've already chosen the best response.
0
good thinking colorful i did that before
colorful
Best Response
You've already chosen the best response.
0
but it doesn't give 5...
wildjay8
Best Response
You've already chosen the best response.
0
radius is 13
colorful
Best Response
You've already chosen the best response.
0
sqrt(13)
wildjay8
Best Response
You've already chosen the best response.
0
which in my notes we had sqrt 18 we put radius as 18
colorful
Best Response
You've already chosen the best response.
0
um... don't know what to tell you about that, sorry :(
colorful
Best Response
You've already chosen the best response.
0
maybe there's a typo, or you copied something wrong?
wildjay8
Best Response
You've already chosen the best response.
0
so answer would be (x-2)^2+(y+4)^2=13
colorful
Best Response
You've already chosen the best response.
0
yeah, looks like it
wildjay8
Best Response
You've already chosen the best response.
0
thank you colorful for helping and pointing out mistake
colorful
Best Response
You've already chosen the best response.
0
no problem :D
welcome!
robtobey
Best Response
You've already chosen the best response.
0
A Mathematica version of the solution with comments and a plot is attached.