Drawing a Hyperbola by Jennifer Silverman
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This applet demonstrates how a hyperbola is constructed. Using GeoGebra commands such as Circle, Intersect, Rotate, and Hyperbola, students can visually see the construction process. Suitable for high school mathematics, particularly in coordinate geometry and function graphing.
GeoGebra Commands & Parameters
Circle(A_2, w) → cCircle(A_2, h) → dLine(A_2, xAxis) → eIntersect(c, e, 2) → B_2Rotate(B_2, α, A_2) → BTangent(B, c) → f,Line(B, A_2) → gIntersect(c, g, 2) → ATangent(A, c) → h_2,Circle(A, h) → kCircle(A, Radius[c]) → pCircle(B, Radius[d]) → qCircle(A, w) → rCircle(B, h) → sIntersect(r, s, 1) → IHyperbola(A, B, I) → tPoint(t) → DIntersect(t, e, 2) → EOrthogonalLine(E, e) → iIntersect(t, e, 1) → FOrthogonalLine(F, e) → jDistance(E, F) → distanceEFCircle(A_2, Segment[A_2, B]) → c_1Intersect(c_1, j, 1) → GOrthogonalLine(G, j) → lIntersect(c_1, j, 2) → HOrthogonalLine(H, j) → mIntersect(c_1, i, 1) → JIntersect(c_1, i, 2) → KPolygon(H, G, J, K) → poly1, h_1, g_1, j_1, k_1Line(J, H) → nLine(G, K) → a_1Segment(D, A) → s_1Segment(D, B) → s_2Segment(A_2, F) → aDistance(E, F) → a_2OrthogonalLine(A_2, a) → b_2Intersect(g_1, b_2) → LSegment(A_2, L) → bCircle(A_1, g_2) → h_3Circle(B_1, e_1) → k_2Intersect(h_3, k_2, 1) → C_1Ellipse(A_1, B_1, C_1) → p_1Line(A_1, B_1) → i_1Point(p_1) → B'_1Segment(A_1, B'_1) → j_2Segment(B_1, B'_1) → l_1Segment(A_1, B_1) → a_3Midpoint(a_3) → G_1OrthogonalLine(G_1, a_3) → b_3Intersect(p_1, b_3) → F_1, E_1Line(A_1, B_1) → c_2Intersect(p_1, c_2) → C_2, D_1Distance(G_1, D_1) → distanceGD_1Distance(G_1, E_1) → distanceGE_1Segment(G_1, E_1) → b_4Segment(G_1, D_1) → a_4
AI Drawing Prompt Reference
Draw a hyperbola with foci at points A and B, which are on opposite sides of line e. Start by drawing two circles c and d, then use rotation and intersection to find the focus I of the hyperbola. Construct the hyperbola t using points A, B, and I, and locate the vertices D and E on line e. Use the perpendicular lines from E and F to find the asymptotes i and j, and finally determine the shape of the hyperbola.
The prompt above was compiled from the original drawing commands and is for reference only.