Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and beginning April 20th, 2021 (Eastern Time) the Yahoo Answers website will be in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.
Trending News
Another Concentric Circle Question?
Need to find the equation to a concentric circle.
x^2 + y^2 = 6x passes through (4, -3)
The answer is x^2 - 6x + y^2 -1 = 0
I do get the above answer if I first write it out as x^2 + y^2 = 6x + 4 - 3 then move everything to the other side but I do have quite the feeling that's the incorrect way to do it.
Thanks to both of you, I sort of see where to go but still somewhat confused while trying to compare this to what is in my text book.
2 Answers
- Mike GLv 78 years agoFavorite Answer
Complete the square for circle given
x^2-6x+9+y^2 = 9
(x-3)^2+y^2 = 3^2
Circle has centre (3,0)
Our concentric circle also has centre (3,0)
Equation is
(x-3)^2+y^2 = r^2 and has a point (4,-3)
1^2 + (-3)^2 = r^2
r^2 = 10
Equation is
(x-3)^2+y^2 = 10
x^2-6x+9+y^2 = 10
x^2-6x+y^2-1 = 0
- PeterLv 48 years ago
x^2 + y^2 = 6x does NOT pass through (4,3). The LHS is 16+9 = 25, the RHS is 6*4 = 24.
The question most is most likely (though not definitely)
x^2 + y^2 + c = 6x
If you substitute in (4, -3) you get c = -1
So x^2 + y^2 -1 = 6x
x^2 + y^2 - 6x - 1 = 0
Which is pretty much what you have done, but without explaining (or possible even understanding) why you have done it.
BTW, this expression can be manipulated as follows:
x^ - 6x + 9 - 10 + y^2 = 0
(x-3)^2 + y^ = 10
Which better shows (IMHO) what the circle looks like - it has radius of sqrt(10) and is centred at (3,0).
