Sponsor Area

Conic Section

Question
CBSEENMA11015587

The differential equation of all circles passing through the origin and having their centres on the x-axis is

  • straight x squared space equals straight y squared space plus space xy dy over dx
  • straight x squared space equals straight y squared space plus space 3 xy dy over dx
  • straight x squared space equals straight y squared space plus space 2 xy dy over dx
  • straight x squared space equals straight y squared space minus space 2 xy dy over dx

Solution

C.

straight x squared space equals straight y squared space plus space 2 xy dy over dx

General equation of all such circles is
x2+ y2 + 2gx = 0.
Differentiating, we get
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