Page 4 - Jose Garcia_2013150017_grade12 ebook

1
BAB CIRCLE

I. Definition and general equation of circle

Attention the picture on the left!

shaped like a wheel and the shape is called a circle. A circle
is defined as the locus of points that are equidistant from a

point. The point is called the center of the circle and the

same distance is called the radius of the circle. Based on the
picture, the center of the circle is (0,0) and one example

of the radius is = .

Based on picture, point ( , ) lies in the circle. so by definition, it must be
0
0
fulfilled :

= =

√( − 0) + ( − 0) =
2
2
0
0
2
2
2
( − 0) + ( − 0) =
0
0
2
0 2 + 0 2 =

if ( , ) run for the whole circle, we get + = which is the equation of a
2
2
2
0
0
circle with center (0,0) and radius .

if you pay attention to the previous picture, it shows the equation of a circle with the
2
2
2
center ( , ) and the radius r is ( − ) + ( − ) = the axes used are the x
′
and y axes. now, what if an image shows two axes namely , and , ′. then it can
be shown that :
- when using the x and y axes. then the equation of a circle with center ( , )
2
2
2
and radius r is ( − ) + ( − ) = .
- when using the x’ and y’ axes. then the equation of a circle with center ( , )
2
2
2
and radius r is ( ′ − ) + ( ′ − ) = .

4 | c o n e s e c t i o n