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the diffrential equation satisfied by all the circles with centres on the line x=y is

the diffrential equation satisfied by all the circles with centres on the line x=y is

Grade:12

1 Answers

Khimraj
3007 Points
6 years ago
equation of circle will be
(x- h)2 + (y-h)2 = r2
diff wrt x
2(x-h) + 2(y-h)*y’ = 0
x-h + yy’ -hy’ =0  – (1)
h = (x + yy’)/(1+y’)
diff equation (1) wrt x.
1 + (y’)2 + yy’’ – hy’’ =0.
put value of h in above equation
(1 + (y’)2 + yy’’)*(1 + y’) = (x + yy’)*y’’.
Hope it clears. If you like answer then please approve it.

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