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Question

The differential equation of the system of circles touching the y-axis at origin is


A

dydx=x2+y22xy

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B

dydx=y2-x2xy

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C

dydx=y2-x22xy

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D

dydx=x2-y22xy

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Solution

The correct option is C

dydx=y2-x22xy


Explanation for the correct option:

Given: The circle touchesy-axis at origin.
The equation of circle that touchesy-axis at origin and has radius a is,
(x-a)2+y2=a2x2+y2-2ax=0
On differentiating with respect to x
2x+2ydydx-2a=0a=x+ydydx
On substituting a in the equation,
x2+y2-2xx+ydydx=0x2+y2-2x2-2xydydx=0y2-x2=2xydydxdydx=y2-x22xy
Hence, the correct answer is option(C)


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