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

1. anonymous

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

2. anonymous

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

3. 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

4. anonymous

oh no wait I remember...

5. anonymous

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

6. anonymous
7. anonymous

8. anonymous

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

9. 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

10. anonymous

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

11. anonymous

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

12. 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|

13. 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...

14. anonymous

yes now i just have to write the equation

15. anonymous

i think we use d formula

16. 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

17. anonymous

radius would be 5 i think

18. anonymous

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

19. anonymous

20. anonymous

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

21. anonymous

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

22. anonymous

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

23. anonymous

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

24. anonymous

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

25. anonymous

good thinking colorful i did that before

26. anonymous

but it doesn't give 5...

27. anonymous

28. anonymous

sqrt(13)

29. anonymous

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

30. anonymous

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

31. anonymous

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

32. anonymous

33. anonymous

yeah, looks like it

34. anonymous

thank you colorful for helping and pointing out mistake

35. anonymous

no problem :D welcome!

36. anonymous

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