Assessment: Written Work 2 Written Work Activity: Exploring the Hyperbola Answer the following for each hyperbola equation below: 1. 4y2 9x2144 - 2. 25(x+4)2-49(y-1)² = 1225 Tasks (for each equation): a. Identify whether the transverse axis is horizontal or vertical. b. Convert the equation to standard form, if necessary. c. Find and label the following: Center, Vertices, Foci, Transverse axis, Conjugate axis, Asymptotes, Endpoint s of the conjugate axis, Endpoints of the latera recta, Lengths of transverse and conjugate axes d. Graph the hyperbola on graphing paper. Include: center, vertices, foci, asymptotes (dashed lines), and both branches. ARACTER
Answer (1)
Answer:1. Equation: a. Transverse axis: Verticalb. Standard form:\frac{y^2}{36} - \frac{x^2}{16} = 1Center: (0, 0)Vertices: (0, ±6)Foci: (0, ±√52) ≈ (0, ±7.21)Transverse axis: VerticalConjugate axis: HorizontalAsymptotes: Latus rectum length: 2. Equation: a. Transverse axis: Horizontalb. Standard form:\frac{(x + 4)^2}{49} - \frac{(y - 1)^2}{25} = 1Center: (-4, 1)Vertices: (-11, 1) and (3, 1)Foci: (-4 ± √74, 1) ≈ (-12.6, 1) and (4.6, 1)Transverse axis: HorizontalConjugate axis: VerticalAsymptotes:y - 1 = ±\frac{5}{7}(x + 4)Note: For graphing, plot center, vertices, foci, and sketch branches using asymptotes as guides.
