Differential Equations Question 298
Question: The differential equation of the family of circles with fixed radius 5 units and centre on the line $ y=2 $ is
Options:
A) $ (y-2)y{{’}^{2}}=25-{{(y-2)}^{2}} $
B) $ {{(y-2)}^{2}}y{{’}^{2}}=25-{{(y-2)}^{2}} $
C) $ {{(x-2)}^{2}}y{{’}^{2}}=25-{{(y-2)}^{2}} $
D) $ (x-2)y{{’}^{2}}=25-{{(y-2)}^{2}} $
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Answer:
Correct Answer: B
Solution:
[b] Circle $ {{(x-h)}^{2}}+{{(y-2)}^{2}}=25 $
$ \Rightarrow 2(x-h)+2(y-2)y’=0\Rightarrow 2(y-2)y’ $
$ =-2(x-h) $
$ \Rightarrow {{(y-2)}^{2}}y{{’}^{2}}={{(x-h)}^{2}}\Rightarrow {{(y-2)}^{2}}y{{’}^{2}}=25-{{(y-2)}^{2}} $
BETA
