Use this calculator to find the point(s) of intersection between a circle and a line given their equations.
The equation of a circle is
\[ (x - h)^2 + (y - k)^2 = r^2 \]where \( (h,k) \) is the center and \( r>0 \) is the radius.
The equation of the line is written in slope–intercept form:
\[ y = mx + b \]where \( m \) is the slope and \( b \) is the y-intercept.
Enter the values of \( h \), \( k \), and \( r \) for the circle, then enter the slope \( m \) and y-intercept \( b \) of the line. Choose the number of decimal places and click Calculate.
The calculator displays the coordinates of up to two intersection points.
Depending on the position of the line relative to the circle, there may be:
Analytical solution for circle–line intersection
Tutorial on the Equation of a Circle
Math Calculators and Solvers
Geometry Calculators