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how should i convert the given equation of ellipse as 16x^2 + 32x + 25 y^2 -100y = 284 into general equation of ellipse , so that i can find out the auxiliary equation of circle ?

how should i convert the given equation of ellipse as 16x^2 + 32x + 25 y^2 -100y = 284 into general equation of ellipse , so that i can find out the auxiliary equation of circle ?

Grade:12th pass

1 Answers

Arun
25750 Points
6 years ago
Dear Sohan
 
16 x^2 + 32 x + 25 y^2 – 100y = 284
16 x^2 + 32 x + 16 + 25 y^2 – 100 y + 100 – 16 – 100 = 284
(4x + 4)^2  +  (5y – 10)^2  =  284 + 100 + 16
(4x + 4)^2  +  (5y – 10)^2  =  400
(4x + 4)^2 / 400 +  (5y – 10)^2 /400 =  1
(x + 1)^2 / 25 +  (y – 2)^2 /16 =  1
hope it helps

Regards
Arun (askIITians forum expert)

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