Let C be the circle center and radius R
A point is on the circle if and only if
which is equivalent to
Going through coordinates
can be written as
Now I think that you can find the center and the radius
Hi! I am new here and need some help. I am doing a maths course at home through Open Uni and I have got stuck.
x^2 + 10x + y^2 - 6y + 9 = 0
represents a circle. Find the centre and it's radius.
I have had a look around online at other examples and it says to put it in a certain format with h,k & r. But I just can't follow it to make the equation given here fit in. Can anyone give me some guidance and help working it out please?
completing the square. That will make these types of problems easy, and it is very useful to know in general.
Complete the square on it so it becomes
(x+5)^2 + (y-3)^2
expand it to show the numbers at the end
-> (5x5) +25 and (-3x-3) +3
x^2 + 10x + 25 + y^2 - 6y + 9 = 25
[the number after the = is 19 because the right side numbers add up to
34 and 34-9 = 25]
so r^2 = 25
therefore, r = 5
so therefore, the centre (h,k) = (-5, 3) [because x+5 = 0 so x must be 5 and y-3 = 0 so y must be 3)
so h = -5 and k = 3
[I think this is right]