Circle and Line Intersection Calculator

Find Intersection Points: Circle & Line with Step-by-Step Solutions

Solve the system of equations to find where a circle and a line meet. Complete step-by-step explanation shown for every calculation.

Formula & method

\[ \text{Circle: } (x - h)^2 + (y - k)^2 = r^2 \] \[ \text{Line: } y = m x + b \]

Substituting \( y = mx + b \) into the circle equation gives:

\[ (x - h)^2 + (mx + b - k)^2 = r^2 \]

Expanding yields a quadratic equation in x:

\[ (1 + m^2) x^2 + (-2h + 2m(b - k)) x + (h^2 + (b - k)^2 - r^2) = 0 \]

The discriminant determines if there are 2, 1 (tangent), or 0 intersection points.

Circle Parameters

\(h\) (x-coordinate of center)

\(k\) (y-coordinate of center)

\(r\) (radius) *

Line Parameters

\(m\) (slope)

\(b\) (y-intercept)

Decimal places

Intersection Points

Enter parameters and press "Find Intersection (Show Steps)"

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Step-by-step solution will appear here after calculation.