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

1. timo86m Group Title

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

2. colorful Group Title

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

3. timo86m Group Title

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. colorful Group Title

oh no wait I remember...

5. colorful Group Title

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

6. timo86m Group Title
7. wildjay8 Group Title

8. colorful Group Title

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

9. timo86m Group Title

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. colorful Group Title

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

11. wildjay8 Group Title

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

12. colorful Group Title

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. colorful Group Title

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. wildjay8 Group Title

yes now i just have to write the equation

15. wildjay8 Group Title

i think we use d formula

16. colorful Group Title

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. wildjay8 Group Title

radius would be 5 i think

18. colorful Group Title

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

19. wildjay8 Group Title

20. wildjay8 Group Title

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

21. colorful Group Title

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

22. wildjay8 Group Title

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

23. colorful Group Title

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

24. wildjay8 Group Title

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

25. wildjay8 Group Title

good thinking colorful i did that before

26. colorful Group Title

but it doesn't give 5...

27. wildjay8 Group Title

28. colorful Group Title

sqrt(13)

29. wildjay8 Group Title

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

30. colorful Group Title

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

31. colorful Group Title

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

32. wildjay8 Group Title

33. colorful Group Title

yeah, looks like it

34. wildjay8 Group Title

thank you colorful for helping and pointing out mistake

35. colorful Group Title

no problem :D welcome!

36. robtobey Group Title

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