Given the ellipse defined by the equation, find the length of the major axis and the minor axis and find the eccentricity. 36x^2+9y^2+72x-36y-2552=0

Tony Burgess 2022-09-14 Answered
Given the ellipse defined by the equation, find the length of the major axis and the minor axis and find the eccentricity.
36 x 2 + 9 y 2 72 x 36 y 252 = 0
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Answers (1)

Aubrie Conley
Answered 2022-09-15 Author has 13 answers
Answer:
36 x 2 + 9 y 2 72 x 36 y 252 = 0 36 ( x 2 + 2 x + 1 ) 36 + 9 ( y 2 4 y + 4 ) 252 = 0 36 ( x + 1 ) 2 + 9 ( y 2 ) 2 = 324 ( x + 1 ) 2 ( 324 / 36 ) + ( y 2 ) 2 ( 324 / 9 ) ) = 1 ( x + 1 ) 2 3 2 + ( y 2 ) 2 6 2 = 1
Here, comparing with standard eclipse
eccentricity = 1 b 2 a 2 = 1 ( 3 6 ) 2 1 1 / 4 = 3 2

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