## anonymous one year ago I have a question, can anybody help me? What is the general form of the equation of the given circle with center A? http://cdn.ple.platoweb.com/PCAP-ASSETS-PROD/258cc385d685420384bc0a8b50aa8568 x2 + y2 + 6x − 24y − 25 = 0 x2 + y2 − 6x + 24y + 128 = 0 x2 + y2 + 6x – 24y + 128 = 0 x2 + y2 + 6x − 24y + 148 = 0

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1. anonymous

The equation of a circle with the center (h, k) and radius r is \[(x-h)^2+(y-k)^2=r^2\] Your center is (-3,12) so that's h and k. Your radius is 5. Plug in the numbers and expand the equation

2. anonymous

(x-(-3)2 + (y-12)2 = 25 right?

3. anonymous

yes

4. anonymous

and what do i do next ? :s

5. anonymous

foil (x+3)² and (y-12)²

6. anonymous

is it (x+9) + (y + 144) = 25 ??

7. anonymous

no. you need to use FOIL for both the x and y (x + 3)² + (y - 12)² = 25 means \[(x+3)(x+3)+(y-12)(y-12)=25\]

8. anonymous

so it would be 6x and 24y right?

9. anonymous

6x and -24y

10. anonymous

okay so we can take out b and c in the answers right?

11. anonymous

yes

12. anonymous

is it a?

13. anonymous

i don't know. I'm not actually working this problem. just following along to make sure your work is right. and now that I look it doesn't look like you can exclude both b and c yet

14. anonymous

Ugh, i suck at math x.x

15. anonymous

what did you get when you multiplied (x+3)(x+3)? you've got to show me something so I can see where you're going wrong

16. anonymous

6x and -24y

17. anonymous

you couldn't have gotten just 6x and -24y. Show me the whole equation

18. anonymous

once we got that part right I can show you how to simplify it into the form they want

19. anonymous

so this is what I got with FOIL (x-3) + (x-3) + (y-12) + (y-12) = 25

20. anonymous

not sure if you have to multiply the 25 too..

21. anonymous

ok. so FOIL is actually multiplication. it stands for First, Inner, Outer, Last. just to help you remember how to distribute. I'm going to show you (x - 3)(x - 3). |dw:1435246652683:dw|

22. anonymous

ok. so FOIL is actually multiplication. it stands for First, Inner, Outer, Last. just to help you remember how to distribute. I'm going to show you (x + 3)(x + 3). |dw:1435246844411:dw|

23. anonymous

all those - should be + because our equation was (x + 3)(x + 3)

24. anonymous

You try with (y -12)(|dw:1435246933731:dw|y-12)

25. anonymous

y2 - 24y + 144

26. anonymous

right. so the equation for the circle becomes \[x^2+6x+9+y^2-24y+144=25\]

27. anonymous

and you combine like terms right?

28. anonymous

yes. don't forget to subtract the 25 from the right side since they want that side to be 0.

29. anonymous

\[x ^{2} + y ^{2} -6x - 24y + 128 = 0\]

30. anonymous

close. +6x :)

31. anonymous

Yaaay!, omg you saved my life, thanks a lot n.n

32. anonymous

no problem

33. anonymous

can you help me out in another question? please ? :c