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Graphing a Hyperbola and Ellipse

Graphing a Hyperbola and Ellipse
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2015-06-23 03:30
Coordinate Geometry
This example demonstrates how to graph the equation 9x^2 – 36x – 4y^2 + 8y = 4. Key mathematical concepts include the properties of conic sections and the graphical representation of equations. Using GeoGebra commands such as LaTeX and Polynomial, the graph of the equation can be constructed. Suitable for high school mathematics courses focusing on coordinate geometry.

GeoGebra Commands & Parameters

  1. LaTeX(steps) → counter
  2. LaTeX("\text{Move the slider to solve the problem.}") → text0
  3. LaTeX("\text{Use the buttons below to return to the original}\cr\text{problem or randomly generate a similar practice}\cr\text{problem.}") → RandomizationText
  4. Corner(1) → A
  5. Corner(3) → B
  6. LaTeX((("\textcolor{#000099}{" * c) * "}")) → Problem
  7. Polynomial((yden / xden * (x - h)) + k) → f
  8. LaTeX((("\textcolor{#000099}{y=" * f) * "}")) → text40
  9. Polynomial((((-yden)) / xden * (x - h)) + k) → g
  10. LaTeX((("\textcolor{#000099}{y=" * g) * "}")) → text40b
  11. Segment(D, E) → d
  12. Segment(F, G) → e
  13. Polygon(C1, C2, C3, C4) → poly1, c1, c2, c3, c4
  14. LaTeX((((((((("\textcolor{#000099}{y-(" * y(C)) * ")=\pm\frac{") * yden) * "}{") * xden) * "}(x-(") * x(C)) * "))}")) → text38
  15. LaTeX((((((((((((((((((((((((("\textcolor{#000099}{" * xfact) * "[x^2-(") * midx) * ")x+") * hsq) * "]") * ypolysign) * "") * yfact) * "[y^2-(") * midy) * ")y+") * ksq) * "]}\cr\text{ }\textcolor{#000099}{ =") * oconst) * "+(") * xfact) * ")(") * hsq) * ")+(") * yfact) * ")(") * ksq) * ")}")) → text12
  16. LaTeX((((((((((((("\textcolor{#000099}{" * xfact) * "[x^2-(") * midx) * ")x+\ldots]") * ypolysign) * "") * yfact) * "[y^2-(") * midy) * ")y+\ldots]=") * oconst) * "}")) → text10
  17. LaTeX((((((((((((("\textcolor{#000099}{" * xfact) * "[x-(") * h) * ")]^2") * ypolysign) * "") * yfact) * "[y-(") * k) * ")]^2 =") * coeffprod) * "}")) → text14
  18. LaTeX((((((((((((((((("\textcolor{#000099}{\frac{" * xfact) * "[x-(") * h) * ")]^2}{") * coeffprod) * "}+\frac{(") * yfact) * ")[y-(") * k) * ")]^2}{") * coeffprod) * "}=\frac{") * coeffprod) * "}{") * coeffprod) * "}}")) → text16
  19. LaTeX((((((((((((("\textcolor{#000099}{" * xsign) * "\frac{[x-(") * h) * ")]^2}{") * xden) * "^2}") * ysign) * "\frac{[y-(") * k) * ")]^2}{") * yden) * "^2}=1}")) → text18
  20. LaTeX((((((((((((("\text{The equation in standard form is }\cr\textcolor{#000099}{" * xsign) * "\frac{[x-(") * h) * ")]^2}{") * xden) * "^2}") * ysign) * "\frac{[y-(") * k) * ")]^2}{") * yden) * "^2}=1}\text{.}")) → text19