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Analytic Geometry

Most assertions in the articles of this section aren’t recorded in any textbooks and for the rest of the assertions, Ali has presented new proofs. As an example, Article 2 shows how to find equations of tangent lines to graphs of polynomial functions, avoiding derivatives, but using the method of long division of polynomials instead.

  • 1. Analytical Geometric Characterizations for Parabolas
  • 2. Finding Tangent Lines to Graphs of Polynomial
    Functions Avoiding Derivatives
  • 3. A Locus Theorem and Its Applications
  • 4. General Inverse Functions, and Slant Line Test
  • 5. Equations of Angle Bisectors for Intersecting Lines
  • 6. Interesting Coordinate Plane Problem and its Solution
  • 7. Lines with Reciprocal Slopes
  • 8. Better Than Line of Best Fit
  • 9. Tangent Lines and Secant Segments for Parabolas
    and Cubic Curves
  • 10. Quick Proof of the Distance From a Point to a Line
  • 11. The Tale of Lady Bugs
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