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$8.00 Pre-calc: Eccentricity and Focal Radii

• From Mathematics: Calculus
• Closed, but you can still post tutorials
• Due on May. 22, 2009
• Asked on May. 19, 2009 at 10:28:06AM

Q:

Completely work through all problems. Show work and diagrams (graphs of hyperbolas) thoroughly. College level Pre-calculus course. Page 824 of fourth edition Pre-calculus text by Dugopolski.

Eccentricity and Focal Radii

For the hyperbola x^2/a^2 - y^2/b^2 = 1, the eccentricity e is defined as e=c/a where a^2 + b^2= c^2. The line segments joining a point on the hyperbola to the foci are called the focal radii.

a: What is the eccentricity of a hyberbola if the asymptotes are perpendicular?

b: Let e sub1 and e sub2 be the eccentricities of the hyperbolas x^2/a^2 - y^2/b^2 = 1 and y^2/b^2 - x^2/a^2=1, respectively. Show that e^2sub1 e^2sub2 = e^2sub1 + e^2sub2.

c: Show that for a point (x sub1, y sub1) on the right hand brach of x^2/a^2 - y^2/b^2 = 1 the lenght of the shorter focal radius is (x sub1 e - a) and the length of the longer forcal radius is (x sub1 e + a)

 

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