## anonymous one year ago All lines 1 unit distant from the origin ANS. (xy'-y)^2 = (1 + (y')^2)

1. anonymous

@ganeshie8

2. anonymous

helo guys

3. anonymous

4. nincompoop

you have multiple post

5. nincompoop
6. anonymous

what is the question here?

7. anonymous

Just a guess: Find an ODE whose general solution is the family of curves that satisfy some property. What that property might be, I'm not so sure. "All lines 1 unit distant from the origin" ? idk what to make of that.

8. anonymous

well, those are just tangent lines to $$x^2+y^2=1$$, so $$2x+2yy'=0\\x+yy'=0\\y'=-\frac{x}y$$so $$\dfrac{dy}{dx}=-\dfrac{x_0}{y_0}$$ which gives $$\frac{y-y_0}{x-x_0}=-\frac{x_0}{y_0}$$