Conic Sections: Geometric Loci and Standard Equations

Master linear equations in general and point-slope forms, calculate perpendicular distances, analyze families of lines, and solve geometric optimization problems on the Cartesian plane.

Analyze circle equations in standard and general forms, determine centers, radii, chord lengths, tangent lines, and intersection properties algebraically.

Understand conics as double-cone cross sections and geometric loci, deriving and graphing standard Cartesian equations of parabolas, ellipses, and hyperbolas.

Classify general second-degree quadratic equations via the algebraic discriminant, rotate coordinate axes, and represent conic sections in polar form.

Model plane curves parametrically, convert between parametric and Cartesian representations, and analyze 2D kinematics, projectile motion, and cycloids.