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Question

Which one of the following differential equations represents the family of straight lines which are at unit distance from the origin?

A
(yxdydx)2=1(dydx)2
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B
(y+xdydx)2=1+(dydx)2
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C
(yxdydx)2=1+(dydx)2
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D
(y+xdydx)2=1(dydx)2
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Solution

The correct option is A (yxdydx)2=1(dydx)2
Consider the equations of the family of straight lines be y=mx+c,
Given that they are at a unit distance from origin,
c=1+m2,
Substituting the value of c gives,
y=mx+1+m2,Which has only one arbitrary constant i.e.,m,
Now,differentiating the equation with respect to x gives,
dydx=m,
y=dydxx+1+(dydx)2
(yxdydx)2=1+(dydx)2 is the differential equation.

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