A Family of Confocal Conics that share a focus are called confocal. Consider the family of conics that have a focus at 10, 12 and a vertex at the origin, as shown in the figure. a. Find equations of two different ellipses that have these properties. b. Find equations of two different hyperbolas that have these properties. c. Explain why only one parabola satisfies these properties. Find its equation.
A Family of Confocal Conics that share a focus are called confocal. Consider the family of conics that have a focus at 10, 12 and a vertex at the origin, as shown in the figure. a. Find equations of two different ellipses that have these properties. b. Find equations of two different hyperbolas that have these properties. c. Explain why only one parabola satisfies these properties. Find its equation.
Chapter11: Conics
Section11.3: Ellipses
Problem 143E: In your own words, define an ellipse and write the equation of an ellipse centered at the origin in...
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A Family of Confocal Conics that share a focus are called confocal. Consider the family
of conics that have a focus at 10, 12 and a vertex at the origin, as shown in the figure.
a. Find equations of two different ellipses that have these properties.
b. Find equations of two different hyperbolas that have these properties.
c. Explain why only one parabola satisfies these properties. Find its equation.
d. Sketch the conics you found in parts (a), (b), and (c) on the same coordinate axes
(for the hyperbolas, sketch the top branches only).
e. How are the ellipses and hyperbolas related to the parabola?
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