Find the Points of Intersection of a Circle with a Line
A tutorial on finding the points of intersection of a circle with a line; general solution.
Example 1
Find the points of intersection of the circle with the line given by their equations(x  2) ^{2} + (y + 3) ^{2} = 4
2x + 2y = 1
Solution to Example 1

We first solve the linear equation for y as follows:
y =  x  1/2

We now substitute y in the equation of the circle by  x  1/2 as follows
(x  2)^{2} + ( x  1/2 + 3)^{2} = 4

We now expand the above equation and group like terms
2 x^{2}  9 x + 25/4 = 0

Solve the above quadratic equation for x to obtain two solutions
x = (9 + √(31)) / 4 and x = (9  √(31)) / 4

We now substitute the values of x already obtained into the equation y =  x  1/2 to obtain the values for y as follows
y = (11  √31) / 4
and y = (11 + √31) / 4

The two points of intersection of the two cirlces are given by
((9 + √(31)) / 4 , (11  √31) / 4 ) and ((9  √(31)) / 4 , (11 + √31) / 4)
Approximated as:(3.64 ,  4.14 ) and (0.86 , 1.36)
Shown below is the graph of the circle, the line and the two points of intersection.
More References and links
Step by Step Math Worksheets Solvers New !Find Points Of Intersection of Circle and Line  Calculator.
Tutorials on equation of circle.
Tutorials on equation of circle (2).
Interactive tutorial on equation of circle.