Concept explainers
Conjecture
Show that the equation of an ellipse can be written as
(b) Use a graphing utility to graph the ellipse
Use the results of part (b) to make a conjecture about the change in the shape of the ellipse as e approaches 0.
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Calculus
- Area of an Ellipse Consider the ellipse x2a2+y2b2=1,a+b=20 (a) The area of the ellipse is given by A=ab. Write the area of the ellipse as a function of a. (b) Find the equation of an ellipse with an area of 264 square centimeters. (c) Complete the table using your equation from part (a), and make a conjecture about the shape of the ellipse with maximum area. (d) Use a graphing utility to graph the area function and use the graph to support your conjecture in part (c).arrow_forwardDISCUSS: Light from a Lamp The light from a lamp forms a lighted area on a wall, as shown in the figure. Why is the boundary of this lighted area a hyperbola? How can one hold a flashlight so that its beam forms a hyperbola on the ground?arrow_forwardThink About It Write an equation whose graph is the bottom half of the hyperbola 9x254x4y2+8y+41=0.arrow_forward
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