Equations of Circle

The Qs are solved as follows:

圖片參考：http://i238.photobucket.com/albums/ff245/chocolate328154/Maths276.jpg?t=1213544374


2008-06-18 12:28:56 補充：
firemouseedward_empi: Excuse me, you are wrong!
For circles to touch internally, difference of radii = distance between centres, i.e.
l r - r1 l = d
When you remove the absolute sign, there are 2 answers, and this time both 1 and 7 are possible.

2008-06-18 12:31:35 補充：
Then for circles to touch externally, sum of radius = distance between centres
And then surely, radius of 1 is not of this case. Let me show you if you still think I am wrong:
sum of radius = 1 + 4 = 5
difference between centres = sqr [ ( 1 - 1 )^2 + ( 1 + 2 )^2 ] = 3 ≠ 5

2008-06-18 12:32:32 補充：
So please have a deeper understanding before you come and point out others' mistakes!

Yes, I also have checked the ans and Gabriella Montez's is correct.
With my and Audrey Hepburn the Elegant's checking, it is most confident.

I have checked both of your answers and I found actually Gabriella Montez's is correct for Q.2.
It is because for two circles to touch each other internally, their differences in radii = distance between the centres.

2008-06-18 13:24:25 補充：
And for r = 7 or 1, both of the answers satisfy the condition. So r = 1 is not rejected.

1) Let r be the radius of the circle, where r is greater than 0.
Since circle C touches the x-axis and the line L, the centre of circle must be (2,r)
Then, by the formula of diatance,
[3(2)+4(r)+9]/5=±r
r=5/3 or -15(rejected)
Therefore, equation of circle C: (x-2)^2+(y-5/3)^2=25/9
2) Centre of given circle=(1,-2)
Radius of given circle=√[1+4-(-11)]=4
Since the two circles touch internally, the two circles must touch at (1,-6) only, which is the minimum point of the given circle.
In order to do that, the required circle must also have a minimum point at (1,-6), i.e. the radius of the required circle is 7.
Therefore, equation of circle: (x-1)^2+(y-1)^2=49

P.S. For finding the equation of circle algebraly, you may follow the steps above (NOT ME).

P.S. Excuse me (Gabriella Montez), but the required circle touches the given cicle internally only, it does not include circle touching the given circle externally. Therefore, sorry to say, but I think the equation of circle with radius of 1 is incorrect.