The equation of a circle is x² + y² = 65

1. The coordinates of its centre are (0 , 0) and the length of its radius is .
   
2. To sketch the circle on grid paper we put the tip of the compasses at the centre (0 , 0) and open them to . To get a length of  consider a point with integral coordinates that the circle will pass through, that is a point with coordinates which are two integers the sum of whose squares is 65. One such point is (4 , 7) because 4² + 7² = 65. You could also approximate the radius by finding  on your calculator and using that as your radius.
                   
   
   
3. The point (5 , 6) is inside the circle because 5² + 6² = 61 and this is less than 65. The distance of (5 , 6) from the centre is less than the radius.
   
   
4. This circle is a horizontal and vertical stretch of the unit circle by a factor of and the mapping rule is  .