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## lissafi 2 years ago show that the two circlex^2+y^2-4x-2y-11=0 and x^2+y^2+20x-12y+72=0 do not intersect.Hint;find the distance between their centers

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1. wio

Use completing the square to get them both in the form of :$(x-h)^2+(y-k)^2=r^2$

2. wio

For example: $x^2-4x = (x-2)^2-4$

3. lissafi

i still cant work it wio

4. Yahoo!

General equation: x^2 + y^2 +2gx + 2hy + c=0 Centre ( -g,-f)

5. Yahoo!

x^2+y^2-4x-2y-11=0 Centre (2,1)

6. Yahoo!

x^2+y^2+20x-12y+72=0 Centre (-10,6)

7. Yahoo!

Hope this will help u..

8. wio

Still gotta find radius though. @Yahoo!

9. Yahoo!

$r=\sqrt{g^2+f^2-c}$

10. wio

You really learn that in class?

11. lissafi

@yahoo how do u get the center x^2+y^2+20x-12y+72=0 Centre (-10,6)?

12. Yahoo!

Compare it with the General equation..

13. Yahoo!

x^2 + y^2 + 2gx + 2fy + c=0 C ( -g,-f) so Here x^2+y^2+20x-12y+72=0 2g = 20 g = 10 2f = -12 f = -6 Since the Centre is -g,-f C ( -10 , - (-6) ) C ( -10 , 6)

14. wio

@lissafi Do you know how to complete the square?

15. lissafi

not on this

16. wio

Just ignore the $$y$$ terms and try to complete the square for (x\), then ignore the $$x$$ terms and complete the square for $$y$$

17. lissafi

wio is that what yahoo did?cos i am lost on this method

18. wio

I dunno what Yahoo! did...

19. wio

$x^2+y^2-4x-2y-11=0$Okay so we just ignore the $$y$$ terms... $x^2-4x-11=0$How do you complete the square here?

20. lissafi

wio i dont know much on completing the square

21. wio

Look it up...

22. Yahoo!

x^2+y^2-4x-2y-11=0 x^2-4x + y^2 -2y = 11 x^2 - 4x + 4 + y^2 - 2y + 1 = 11 + 4 + 1 (x-2)^2 + (y-1)^2 = 16 (x-2)^2 + (y-1)^2 = 4^2 now it is a circle with centre (2,1) and radius 4

23. Yahoo!

@lissafi u got it..now

24. lissafi

yap,and for x^2+y^2+20x-12y+72=0?

25. Yahoo!

Try it out...

26. lissafi

i lost in (x-2)^2 + (y-1)^2 = 16

27. lissafi

i know you add +4+1 on both side

28. Yahoo!

Since we added 4 and 1 on LHS we have to do in RHS tooooo

29. lissafi

i know you can find x to subtitute to get y and have the points,but i dont know this method

30. sirm3d

in $x^2+y^2+20x-12y+72=0$ what term must be added to $x^2+20x$ to get a perfect square trinomial that can be written in the form $(x+\_\_)^2$

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