Investigation 6: The Equation of a Circle
Test yourself (solution)
The equation of a circle is x2 + y2 = 65
- The coordinates of its centre are (0 , 0) and the length of its
radius is
 .
- 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.
- 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.
- This circle is a horizontal and vertical stretch of the unit
circle by a factor of
and the mapping rule is
 .
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