[SOLVED] Checking: Circle Equations Questions Last time I got people to check my homework here, I got things marked wrong when they where said to be right. Lets see if it happens again... 1. The problem statement, all variables and given/known data (1) The circle C has centre (3, 4) and passes through the point (8, 8). Find an equation for C. (2) Find the centre and radius of the circle x² + y² + 4x + 6y – 17 = 0 (3) A(4, 0) and B(3, 5) are the end points of a diameter of the circle C. Find (a) the exact length of AB, (b) the coordinates of the midpoint P of AB, (c) an equation for the circle C. 2. Relevant equations None 3. The attempt at a solution Right here is my working for (1) Since we know the circle centre and a point the circle passes through, I can use pythag to work on the radius right? It seems a little too simple to work, but I can't see anything wrong with it. After drawing a clear diagram; (4+8)² + 5² = r² r² = 144 + 25 r² = 169 r = 13 Therefore the equation must be (x-3)² + (y-4)² = 13 Correct? Now, my working for (2); The equation needs to be factorised, so I have to "complete the square" to get the stuff inside the brackets. This is usually where I go wrong, so check this bit carefully please! (x+2)² - 4 + (y+3)² - 9 - 17 = 0 Rearraged: (x+2)² + (y+3)² = 17 Ah, I have to go now, but I'll post the answers to 3 quickly: a) I got 5.09 b) x = 3.5 y = 2.2 and c) (x+3.5)² + (y+2.2)² = 5.09 Sorry about that lack of working out. Thank you for your time if you've read this far!