The circle C has centre A (10, 12) and passes through the point B (15, 15). a) Find the length of AB, giving your answer as a simplified surd. b) Hence write down an equation for C in the form (x+c)^2 + (y+d)^2 = r^2.
a) Given two coordinate pairs (x1, y1) and (x2, y2) you can work out the distance AB as sqrt((x1-x2)2+(y1-y2)2) - subbing in values gives us sqrt(52+32) which is equal to sqrt(34). Despite the question asking for a "simplifed" surd, sqrt(34) cannot be simplified any further so sqrt(34) is the final answer. b) The answer from a) gives us the radius r. The equation form given is where (-c, -d) is the centre, and r is the radius. Thus, the equation is: (x-10)2+(y-12)2=34
