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A hyperbola with equation of the form (y^2 / a^2) - (x^2 / b^2) = 1 contains the point...
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Since the point are located on the hyperbolla, then its coordinates verify the equation of hyperbolla.
45/4a^2 - 9/b^2 = 1 <=> 45b^2/4 - 9a^2 = a^2*b^2 (1)
18/a^2 - 16/b^2 = 1 <=> 18b^2 - 16a^2 = a^2*b^2 (2)
We'll equate (1) and (2):
45b^2/4 - 9a^2 = 18b^2 - 16a^2
18b^2 - 45b^2/4 = 16a^2 - 9a^2
27b^2 = 28a^2
a^2 = 27b^2/28 (3)
We'll replace (3) into (2):
18*28/27b^2 - 16/b^2 = 1
56-48 = 3b^2
3b^2 = 8
b^2 = 8/3
a^2 = 27*8/3*28
a^2 = 18/7
The sum of the squares is: a^2 + b^2 = 8/3 + 18/7 = 110/21
Posted by giorgiana1976 on May 24, 2011 at 2:06 AM (Answer #1)
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