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Circle Maths help.

Got a example question in a lecture today and I don't understand it. Could someone help please?

I need to find the center and the radius of this circle.
x^2-4x+y^2+10y-7=0

so I was told that this was how it goes...
(x^2-4x+4)+(y^2+10y+25)=7+4+25

(x-2)^2+(y+5)^2=36

6^2=36

But I don't understand where the +4 and the +25 come from in the first line of working. Any help appreciated. :smile:
Reply 1
Avatar for TenOfThem
TenOfThem
18
Original post by Guru Jason
Got a example question in a lecture today and I don't understand it. Could someone help please?

I need to find the center and the radius of this circle.
x^2-4x+y^2+10y-7=0

so I was told that this was how it goes...
(x^2-4x+4)+(y^2+10y+25)=7+4+25

(x-2)^2+(y+5)^2=36

6^2=36

But I don't understand where the +4 and the +25 come from in the first line of working. Any help appreciated. :smile:



This is A Level, not undergraduate

But the bit you are asking about is Completing the Square which is GCSE knowledge

Do you know that

(x+a)2=x2+2ax+a2(x+a)^2 = x^2 + 2ax + a^2

and, therefore, that

x2+2ax=(x+a)2−a2x^2 + 2ax = (x+a)^2 - a^2
Reply 2
Avatar for Guru Jason
Guru Jason
OP
21
Original post by TenOfThem
This is A Level, not undergraduate

But the bit you are asking about is Completing the Square which is GCSE knowledge

Do you know that

(x+a)2=x2+2ax+a2(x+a)^2 = x^2 + 2ax + a^2

and, therefore, that

x2+2ax=(x+a)2−a2x^2 + 2ax = (x+a)^2 - a^2


Thanks. It's a foundation year so I suppose it would be A level. :smile:
Reply 3
Avatar for TenOfThem
TenOfThem
18
Original post by Guru Jason
Thanks. It's a foundation year so I suppose it would be A level. :smile:


Ah - ok :smile:

So did you understand what I said or do you want me to go slower
Reply 4
Avatar for Guru Jason
Guru Jason
OP
21
Original post by TenOfThem
Ah - ok :smile:

So did you understand what I said or do you want me to go slower


I think I got it now. I should be able to do the rest (the radius bit) of the questions now. Thanks.
Reply 5
Avatar for TenOfThem
TenOfThem
18
Original post by Guru Jason
I think I got it now. I should be able to do the rest (the radius bit) of the questions now. Thanks.


ok :smile:

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