aivantettet26 one year ago Show that the family of circles (x+1)^2+(y-3)^2 = c^2 can be interpreted as two families of solution of the differential equations dy/dx = -(x-1)/y-3

1. aivantettet26

$\frac{ dy }{ dx } = \frac{ -(x+1) }{ y-3 }$

2. anonymous

The proof is as follows. I hope u know Chain Rule and that differentiation is a linear function. Sorry for the picture being a bit hazy.

3. IrishBoy123

you can also solve the DE, it is clearly separable. in fact, that might be much easier as you can complete the square

4. anonymous

yeah... that's an option too... but arranging it into the standard form for a circle would be tedious @IrishBoy123

5. IrishBoy123