Circles from Given Conditions and Position of a Point

Find the centre and radius, then substitute into the standard equation. **Given** | **Method** | **Example** Centre and one point on the circle | r2= squared distance from the centre to the point. | Centre (2,-1), through (4,3) r2=(4-2)2+(3-(-1))2=20 (x-2)2+(y+1)2=20 Endpoints of a diameter | Centre = midpoint of the endpoints. r2= squared distance from the centre to either endpoint. | A(-3,2), B(5,6) Centre =(-3+52, 2+62)=(1,4) r2=(5-1)2+(6-4)2=20 (x-1)2+(y-4)2=20 Position of a point d2=(x_P-a)2+(y_P-b)2 **Position** | **Condition** Inside | d2r2 For the diagram: CP2=5<16, CQ2=16, CR2=34>16.