Find the Points of Intersection of a Circle and a Line

Find the intersection points of a circle \((x - h)^2 + (y - k)^2 = r^2\) and a line \(ax + by = c\). Generate random problems, see detailed algebraic steps with exact values, and visualize the circle, line, and intersection points.

📐 Circle-Line Intersection Finder

Find intersection points of \((x - h)^2 + (y - k)^2 = r^2\) and \(ax + by = c\)

Circle: \( (x)^2 + (y)^2 = 4 \), Line: \( x + y = 2 \)
Find the intersection points (if any). Click "Show me" for each step.

📖 Step-by-Step Solution

STEP 1: Solve the line equation for y
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STEP 2: Substitute into the circle equation
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STEP 3: Expand and simplify to quadratic form
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STEP 4: Solve the quadratic and find intersection points
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📊 Graphical Visualization
Green: Circle | Blue: Line | Red points: Intersections

Adjust axis scale to see the intersection points clearly.