Q.

The differential equation of all ellipses centred at the origin is

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a

y2+xy12yy1=0

b

xyy2+xy12yy1=0

c

yy2+xy12xy1=0

d

xy2+xy12yy1=0

answer is B.

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Detailed Solution

Ellipses centred at origin are given by  x2a2+y2b2=1

2xa2+2yb2y1=0 xa2+yb2y1=0

Differentiating again, we have

1a2+1b2y12+yy2=0

Multiplying (iii) with x and then subtracting from (ii) we have 

1/b2yy1xy12xyy2=0 xyy2+xy12yy1=0

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