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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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undeadable | (Level 1) Honors

Posted May 24, 2011 at 1:10 AM via web

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A hyperbola with equation of the form (y^2 / a^2) - (x^2 / b^2) = 1 contains the point (3, 3sqrt5 / 2) and ( -4, 3sqrt2). Find a^2+b^2.sqrt = square root I tried to work this out.

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted May 24, 2011 at 2:06 AM (Answer #1)

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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

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