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Advanced Cartesian Lines, Circles, and Tangent-Normal Systems

12th Grade · Math · Open Global Math

10 lessons

Goal

Analyze straight lines, general and standard forms of circles, and solve geometric problems involving tangents, normals, and intersections.

10 lessons
0 of 10 done
  1. Point-Slope and General Linear Equations in Cartesian SpaceUp next
  2. Parallel and Perpendicular Line Criteria and Families of LinesNot started yet
  3. Perpendicular Distance from a Point to a LineNot started yet
  4. Standard Form of a Circle Centered at (h, k)Not started yet
  5. Converting General Circle Equations by Completing the SquareNot started yet
  6. Equations of Tangent Lines to Circles at a Given PointNot started yet
  7. Equations of Normal Lines to CirclesNot started yet
  8. Finding Tangents to a Circle from an External PointNot started yet
  9. Intersections of Lines and Circles: Secants and ChordsYou are here
  10. Solving Real-World Geometric Boundary Problems with CirclesNot started yet
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Learning standards covered

GlobalOGM.13.GEO.1Open Global Math Standards 2026™ · 12th Grade

Analyze straight lines in Cartesian space ($y - y_1 = m(x - x_1)$, $ax + by + c = 0$), including parallelism and perpendicularity criteria, and circles in standard and general form $(x - a)^2 + (y - b)^2 = r^2$ using completing the square and geometric tangent/normal properties.