String Hyperbola Construction and Geometric Relations
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This example demonstrates how to construct a hyperbola in GeoGebra while using string labels to display its geometric properties. The core mathematical concepts include the definition of a hyperbola (constant difference of distances to two foci), foci, transverse and conjugate axes, and parametric relations of conic sections. Construction highlights: commands such as Distance, Circle, Point, LineBisector, Line, Intersect are used to create base points and auxiliary lines; Ellipse and Hyperbola commands draw the conics; Sequence, Length, Element, and If manage point lists and conditional logic for dynamic string output. Suitable for high school or college analytic geometry courses, it helps visualize hyperbola generation and its connections to ellipses, complex numbers, confidence intervals, and other topics, while also serving as an advanced GeoGebra construction tutorial.
GeoGebra Commands & Parameters
Distance(C, A) → bCircle(A, B, xOyPlane) → cPoint(c) → DLineBisector(C, D, xOyPlane) → gLine(A, D) → fIntersect(g, f) → EEllipse(C, A, E, xOyPlane) → eHyperbola(A, C, E, xOyPlane) → dSequence(Rotate[B, i, A], i, 0°, 360°, 6°) → list1Length(list1) → aSequence(LineBisector[Element[list1, i], C, xOyPlane], i, 1, a) → list2Element(list2, A1) → B1Element(list2, A2) → B2Element(list2, A3) → B3Element(list2, A4) → B4Element(list2, A5) → B5Element(list2, A6) → B6Element(list2, A7) → B7Element(list2, A8) → B8Element(list2, A9) → B9Element(list2, A10) → B10Element(list2, A11) → B11Element(list2, A12) → B12Element(list2, A13) → B13Element(list2, A14) → B14Element(list2, A15) → B15Element(list2, A16) → B16Element(list2, A17) → B17Element(list2, A18) → B18Element(list2, A19) → B19Element(list2, A20) → B20Element(list2, A21) → B21Element(list2, A22) → B22Element(list2, A23) → B23Element(list2, A24) → B24Element(list2, A25) → B25Element(list2, A26) → B26Element(list2, A27) → B27Element(list2, A28) → B28Element(list2, A29) → B29Element(list2, A30) → B30Element(list2, A31) → B31Element(list2, A32) → B32Element(list2, A33) → B33Element(list2, A34) → B34Element(list2, A35) → B35Element(list2, A36) → B36If(b > 1, Eccentricity[d], Eccentricity[e]) → C2Element(list2, A37) → B37If(b > 1, Eccentricity[d], Eccentricity[e]) → C3If(b > 1, Eccentricity[d], Eccentricity[e]) → C4If(b > 1, Eccentricity[d], Eccentricity[e]) → C5If(b > 1, Eccentricity[d], Eccentricity[e]) → C6If(b > 1, Eccentricity[d], Eccentricity[e]) → C7If(b > 1, Eccentricity[d], Eccentricity[e]) → C8If(b > 1, Eccentricity[d], Eccentricity[e]) → C9If(b > 1, Eccentricity[d], Eccentricity[e]) → C10If(b > 1, Eccentricity[d], Eccentricity[e]) → C11If(b > 1, Eccentricity[d], Eccentricity[e]) → C12If(b > 1, Eccentricity[d], Eccentricity[e]) → C13If(b > 1, Eccentricity[d], Eccentricity[e]) → C14If(b > 1, Eccentricity[d], Eccentricity[e]) → C15If(b > 1, Eccentricity[d], Eccentricity[e]) → C16If(b > 1, Eccentricity[d], Eccentricity[e]) → C17If(b > 1, Eccentricity[d], Eccentricity[e]) → C18If(b > 1, Eccentricity[d], Eccentricity[e]) → C19If(b > 1, Eccentricity[d], Eccentricity[e]) → C20If(b > 1, Eccentricity[d], Eccentricity[e]) → C21If(b > 1, Eccentricity[d], Eccentricity[e]) → C22If(b > 1, Eccentricity[d], Eccentricity[e]) → C23If(b > 1, Eccentricity[d], Eccentricity[e]) → C24If(b > 1, Eccentricity[d], Eccentricity[e]) → C25If(b > 1, Eccentricity[d], Eccentricity[e]) → C26If(b > 1, Eccentricity[d], Eccentricity[e]) → C27If(b > 1, Eccentricity[d], Eccentricity[e]) → C28If(b > 1, Eccentricity[d], Eccentricity[e]) → C29If(b > 1, Eccentricity[d], Eccentricity[e]) → C30If(b > 1, Eccentricity[d], Eccentricity[e]) → C31If(b > 1, Eccentricity[d], Eccentricity[e]) → C32If(b > 1, Eccentricity[d], Eccentricity[e]) → C33If(b > 1, Eccentricity[d], Eccentricity[e]) → C34If(b > 1, Eccentricity[d], Eccentricity[e]) → C35If(b > 1, Eccentricity[d], Eccentricity[e]) → C36If(b > 1, Eccentricity[d], Eccentricity[e]) → C37If(b > 1, Eccentricity[d], Eccentricity[e]) → C1If(b > 1, Eccentricity[d], Eccentricity[e]) → C38If(b > 1, Eccentricity[d], Eccentricity[e]) → C39If(b > 1, Eccentricity[d], Eccentricity[e]) → C40If(b > 1, Eccentricity[d], Eccentricity[e]) → C41If(b > 1, Eccentricity[d], Eccentricity[e]) → C42If(b > 1, Eccentricity[d], Eccentricity[e]) → C43If(b > 1, Eccentricity[d], Eccentricity[e]) → C44If(b > 1, Eccentricity[d], Eccentricity[e]) → C45If(b > 1, Eccentricity[d], Eccentricity[e]) → C46Element(list2, A38) → B38Element(list2, A39) → B39Element(list2, A40) → B40Element(list2, A41) → B41Element(list2, A42) → B42Element(list2, A43) → B43Element(list2, A44) → B44Element(list2, A45) → B45Element(list2, A46) → B46If(b > 1, Eccentricity[d], Eccentricity[e]) → C47If(b > 1, Eccentricity[d], Eccentricity[e]) → C48If(b > 1, Eccentricity[d], Eccentricity[e]) → C49If(b > 1, Eccentricity[d], Eccentricity[e]) → C50If(b > 1, Eccentricity[d], Eccentricity[e]) → C51If(b > 1, Eccentricity[d], Eccentricity[e]) → C52If(b > 1, Eccentricity[d], Eccentricity[e]) → C53If(b > 1, Eccentricity[d], Eccentricity[e]) → C54If(b > 1, Eccentricity[d], Eccentricity[e]) → C55If(b > 1, Eccentricity[d], Eccentricity[e]) → C56If(b > 1, Eccentricity[d], Eccentricity[e]) → C57If(b > 1, Eccentricity[d], Eccentricity[e]) → C58If(b > 1, Eccentricity[d], Eccentricity[e]) → C59If(b > 1, Eccentricity[d], Eccentricity[e]) → C60If(b > 1, Eccentricity[d], Eccentricity[e]) → C61Element(list2, A47) → B47Element(list2, A48) → B48Element(list2, A49) → B49Element(list2, A50) → B50Element(list2, A51) → B51Element(list2, A52) → B52Element(list2, A53) → B53Element(list2, A54) → B54Element(list2, A55) → B55Element(list2, A56) → B56Element(list2, A57) → B57Element(list2, A58) → B58Element(list2, A59) → B59Element(list2, A60) → B60Element(list2, A61) → B61