Circle

A circle is the set of all points that are an equal distance (radius) from a given point (centre). In other words, every point on the circumference of a circle is equidistant from its centre.

Equation of a circle with centre at the origin:

If P(x,y) is a point on a circle with centre O(0,0) and radius r, then the equation of the circle is:

$$ x^2+y^2=r^2 $$

Example:

Find the equation for the circle with centre (0,0) and radius 3

Solution:

x²+y²=r²

x²+y²=3²

x²+y²=9

The standard equation of a circle:

If P(x,y) is a point on a circle with centre (h,k) and radius r, then the equation of the circle is:

$$ (x−h)^2+(y−k)^2=r^2 $$

Example:

Find the equation of the circle with centre (1,2) and radius 3

Solution:

(x−1)²+(y−2)²=3²

(x²−2x+1)+(y²−4y+4) =9

x²+y²−2x−4y−4=0