Finding the Standard Form of an Ellipse

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. Vector(Center, MinNeg) → minNeg
7. Vector(Center, MajNeg) → majNeg
8. Vector(Center, MajPos) → majPos
9. Vector(Center, MinPos) → minPos
10. LaTeX((((((("\text{The minor axis runs } " * minorOrientation) * "\text{ from }") * MinNeg) * "\text{ to }\cr ") * MinPos) * "\text{.}")) → text4
11. If(xden < yden, LaTeX["b^2"], LaTeX["a^2"]) → xdenom
12. If(x(Center) ≠ 0, LaTeX["(x-x_0)^2"], LaTeX["x^2"]) → xnum
13. If(y(Center) ≠ 0, LaTeX["(y-y_0)^2"], LaTeX["y^2"]) → ynum
14. If(xden < yden, LaTeX["a^2"], LaTeX["b^2"]) → ydenom
15. LaTeX((((((((("\frac{" * xnum) * "}{") * xdenom) * "}+\frac{") * ynum) * "}{") * ydenom) * "}=1")) → structure
16. LaTeX((((((((((((("\text{In the graph, the major axis runs " * majorOrientation) * " from }\cr\textcolor{#000099}{") * MajNeg) * "}\text{ to }\textcolor{#000099}{") * MajPos) * "}\text{ and has a length of }\textcolor{#000099}{") * major) * "}\text{.}\cr\text{Therefore, the value of }\textcolor{#000099}{a}\text{ is half of }\textcolor{#000099}{") * major) * "}\text{, or }\textcolor{#000099}{") * semimajor) * "}\text{.}")) → text13
17. LaTeX((((((((((((("\text{In the graph, the minor axis runs " * minorOrientation) * " from }\cr\textcolor{#000099}{") * MinNeg) * "}\text{ to }\textcolor{#000099}{") * MinPos) * "}\text{ and has a length of }\textcolor{#000099}{") * minor) * "}\text{.}\cr\text{Therefore, the value of }\textcolor{#000099}{b}\text{ is half of }\textcolor{#000099}{") * minor) * "}\text{, or }\textcolor{#000099}{") * semiminor) * "}\text{.}")) → text16
18. LaTeX("\text{Since the ellipse is centered at the origin, all the}\cr\text{information about the center is in the form of the}\cr\text{equation used to describe the ellipse.}") → text17
19. LaTeX((((("\text{The point }\textcolor{#000099}{(x_0,y_0)}\text{ in the equation for an ellipse not}\cr\text{centered at the origin is the center of the ellipse.}\cr\text{Therefore, }\textcolor{#000099}{x_0=" * x(Center)) * "}\text{ and }\textcolor{#000099}{y_0=") * y(Center)) * "}\text{.}")) → text17a
20. LaTeX((((((("\text{For this ellipse, the longer axis is the axis that}\cr\text{runs }" * majorOrientation) * "\text{ from }") * MajNeg) * "\text{ to }") * MajPos) * "\text{.}\cr\text{This is the major axis.}")) → text3
21. If(y(Center) ≠ 0, LaTeX[(("(y-" * y(Center)) * ")^2")], LaTeX["y^2"]) → ynumSub
22. If(x(Center) ≠ 0, LaTeX[(("(x-" * x(Center)) * ")^2")], LaTeX["x^2"]) → xnumSub
23. LaTeX((("\text{Therefore, the correct formula to use is }\cr" * structure) * "\text{, for which }\textcolor{#000099}{a}\text{ is half the}\cr\text{length of the major axis and }\textcolor{#000099}{b}\text{ is half the length}\cr\text{of the minor axis.}")) → text10