MATH 101 Study Guide - Midterm Guide: Asymptote, Trigonometric Functions, Hyperbola

• School: UBC
• Department: Mathematics
• Course: MATH 101
• Professor: Christopher Friedrichs

Document Summary

Draw a positive hyperbola and label it : (conjugate axis, transverse axis) If a = b, the hyperbola is a rectangular hyperbola (square) If ac > 0, then the conic is an ellipse (if a = c circle) If ac < 0, then the conic is a hyperbola (if a = -c rectangular) If ac = 0, then the conic is a parabola (if a=0 horizontal and if c=0 vertical) The diagram shows the semi-elliptical cross section of a tunnel. The two vertical 3 meter support posts are equidistant from the center c of the tunnel and the two 6 meter beams meet at the highest point of the tunnel. If the maximum height of the tunnel is 5 meters, determine the width of ab of the tunnel. A rectangle with a length three times its width is inscribed in the ellipse determine the area of the rectangle if its longer side is horizontal.