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Analytic Geometry

Analytic Geometry. Conic Sections. Parabolas, hyperbolas, ellipses, circles. Analytic geometry, usually called coordinate geometry and earlier referred to as Cartesian geometry or analytical geometry, is the study of geometry using the principles of algebra. Analytic Geometry.

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Analytic Geometry

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  1. Analytic Geometry • Conic Sections Parabolas, hyperbolas, ellipses, circles

  2. Analytic geometry, usually called coordinate geometry and earlier referred to as Cartesian geometry or analytical geometry, is the study of geometry using the principles of algebra Analytic Geometry

  3. The plane that intersects the cone is perpendicular to the axis of symmetry of the cone. The Circle

  4. The plane that intersects the cone is neither parallel nor perpendicular to the axis of symmetry of the cone and cuts through 2 “sides” The Ellipse

  5. The plane that intersects the cone is parallel to an element of the cone. The Parabola

  6. The plane that intersects the cone is parallel to the axis of symmetry of the cone. The Hyperbola

  7. Where do you see conics in real life?

  8. z y a 0 b x y x Dimensions 1D 2D 3D

  9. I IV III II b (a,-b) (-a,b) (-a,-b) (a,b) a Ordered Pairs Review : (a,b)

  10. Finding the inclination of a line Θ=0 Θ Θ Θ=∏/2 Horizontal Vertical Acute Obtuse

  11. Θ Example: make sure you are in radian mode Find the inclination of the line 2x+3y = 6 m= -a/b m= -2/3 Θ = ∏ + arctan (-2/3) Θ = ∏ +(-.588) Θ = 2.554

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