ART A sculpture has a hyperbolic cross section (see figure). (a) Write an equation that models the curved sides of the sculpture. (b) Each unit in the coordinate plane represents 1 foot. Find the width of the sculpture at a height of 5 feet.
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A standard equation for a hyperbola with a horizontal axis is: (x-h)^2/a^2 - (y-k)^2/b^2 = 1 In this case, the center of the hyperbola is at the origin (0,0), so h = 0 and k = 0. The vertices of the hyperbola are at points (a,0) and (-a,0). From the figure, we Show more…
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Art A sculpture has a hyperbolic cross section (see figure). (a) Write an equation that models the curved sides of the sculpture. (b) Each unit in the coordinate plane represents 1 foot. Find the width of the sculpture at a height of 5 feet.
Topics in Analytic Geometry
Hyperbolas
A cross section of a sculpture can be modeled by a hyperbola (see figure). (FIGURE CAN NOT COPY) (a) Write an equation that models the curved sides of the sculpture. (b) Each unit in the coordinate plane represents 1 foot. Find the width of the sculpture at a height of 18 feet.
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