Exam 4 Solutions Sp10 (1)

Since a 2 b 2 c2 then which tells us that the foci

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Unformatted text preview: ertices are (7, –3) and (7, –5). Since a 2 + b 2 = c2, then , which tells us that the foci are and . The asymptotes are the lines that pass through the center and have slopes equal to ± a/b. Those are and . Here is a sketch. y x 4. Find the equation of the line tangent to the ellipse through the point . We need a point and a slope. We have a point, . To get the slope we should evaluate dy/dx at the point in question. So, to get started, I need dy/dx, which I can get using implicit differentiation. So the slope of the tangent line is . And the (unsimplified) equation of the tangent line is . 5. The region bounded by the hyperbola and the vertical line through its right-most focus is revolved about the x-axis. Set up the definite integral needed to find the volume of the resulting solid. (You do not need to evaluate this integral.) First a sketch. In preparation for the sketch: From the formula I can "read off" . So the center is (0, 0), the vertices are at (–3, 0) and (3, 0), and the foci are at and And the hyperbola has asymptotes , which you really don't need for the purposes...
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This document was uploaded on 03/18/2014 for the course MATH 237 at Frostburg.

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