Circle. Center of circle. Radius of circle.
Equation of circle. Equation of tangent line to circle.
Tangency condition of straight line and circle.
A circle ( Fig.1 ) is a locus of points, equidistant from the given point Î , called a center of circle , at the distance R . A number R > 0 is called a radius of circle .
An equation of circle of radius R with a center in a point Î ( õ 0 , ó 0 ) is:
( õ – õ 0 ) 2 + ( ó – ó 0 ) 2 = R 2 .
If a center of the circle coincides with the origin of coordinates , then an equation of circle becomes :
õ 2 + ó 2 = R 2 .
Let Ð ( õ 1 , ó 1 ) be a point of the circle ( Fig.1 ), then an equation of tangent line to circle in the given point is:
( õ 1 – õ 0 ) ( õ – õ 0 ) + ( ó 1 – ó 0 ) ( ó – ó 0 ) = R 2 .
A tangency condition of a straight line y = m x + k and a circle õ 2 + ó 2 = R 2 :
k 2 / ( 1 + m 2 ) = R 2 .