The elements of coordinate geometry, by S. L. Loney, M.A.

CHAPTER VIII.

THE CIRCLE.
138. Def. A circle is the locus of a point which
moves so that its distance from a fixed point, called the
centre, is equal to a given distance. The given distance is
called the radius of the circle.
139. To find the equation to a circle, the axes of coordinates being two straight lines through its centre at right
angles.
Let 0 be the centre of the circle and let a be its radius.
Let OX and OY be the axes of
coordinates. Y
Let P be any point on the circum-
ference of the circle, and let its coordinates be x and y.
Draw PMperpendicular to OX and \ / 1 X
join OP.
Then (Euc. I. 47)
OM2 + MP2 = a2,
i. e. x2 + y2 = a2.
This'being the relation which holds between the coordinates of any point on the circumference is, by Art. 42, the
required equation.
140. To find the equation to a circle referred to any
rectangular axes,