wildjay8 3 years ago Write the equation of a circle that has center (2,-4) and passing through (4,-1)

1. timo86m

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

2. colorful

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

3. timo86m

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

oh no wait I remember...

5. colorful

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

6. timo86m
7. wildjay8

8. colorful

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

9. timo86m

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

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

11. wildjay8

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

12. colorful

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

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

yes now i just have to write the equation

15. wildjay8

i think we use d formula

16. colorful

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

radius would be 5 i think

18. colorful

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

19. wildjay8

20. wildjay8

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

21. colorful

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

22. wildjay8

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

23. colorful

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

24. wildjay8

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

25. wildjay8

good thinking colorful i did that before

26. colorful

but it doesn't give 5...

27. wildjay8

28. colorful

sqrt(13)

29. wildjay8

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

30. colorful

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

31. colorful

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

32. wildjay8

33. colorful

yeah, looks like it

34. wildjay8

thank you colorful for helping and pointing out mistake

35. colorful

no problem :D welcome!

36. robtobey

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