SMA 103 • ANALYTICAL GEOMETRY

Cartesian Coordinate System and Distance Formula Internal and External Division of Line Segments Gradient, Slope-Intercept, and Normal Forms Parallel and Perpendicular Lines Angle Between Two Intersecting Lines Perpendicular Distance from a Point to a Line

Standard Equation of a Circle (Center and Radius) General Equation of a Circle Circle Passing Through Three Non-Collinear Points Equations of Tangent and Normal to a Circle Length of Tangent from an External Point Intersection of Lines and Circles

Polar Coordinate System Definition and Representation Conversion Between Cartesian and Polar Coordinates Transforming Cartesian Equations to Polar Form Transforming Polar Equations to Cartesian Form Polar Equations of Lines and Circles Graphing Polar Curves and Symmetry Analysis

Conic Section Definition and Standard Forms Focus, Directrix, Vertex, and Axis of Symmetry Length and Equation of Latus Rectum Translated Parabolas with Vertex (h, k) Equations of Tangent and Normal to a Parabola Parametric Equations and Geometric Properties

Standard Equation of an Ellipse (Center at Origin) Major and Minor Axes, Vertices, and Foci Directrices, Eccentricity, and Latus Rectum Translated Ellipses with Center (h, k) Equations of Tangent and Normal to an Ellipse Parametric Equations of an Ellipse

Standard Equation and Geometric Definition Transverse and Conjugate Axes, Vertices, and Foci Directrices, Eccentricity, and Latus Rectum Asymptotes of a Hyperbola and Rectangular Hyperbolas Translated Hyperbolas with Center (h, k) Equations of Tangent and Normal to a Hyperbola

Radian Measure and Circular Functions Fundamental Pythagorean and Quotient Identities Compound-Angle and Double-Angle Formulas Factor Formulas (Sum-to-Product and Product-to-Sum) The Half-Angle t-Substitution (Weierstrass) Solving Trigonometric Equations and General Solutions