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A curve passes through the point (1,1) and has the property that the normal at any point on the curve is equidistant from the x-axis and the origin. Form the differential equation for the curve, find the curve and state which quadrant(s) the curve lies in.

Here is what I did,

The slope of the normal at any point would be -1/(dy/dx) and the equation of the normal at the point would be y=mx+c where m= -1/(dy/dx). If this is the normal at (1,1), then 1=m+c, => c=1-m

Therefore, the equation of the line comes out to be y=mx+1-m. Rearranging this, y-mx-1+m=0. The distance of this line from the origin is :

|-1+m| / ((1+m*m)^1/2) which is equal to 1 (distance from the x-axis as this is the normal at (1,1) ).

After this, you substitute m= -1/(dy/dx) and you get your differential equation... only you dont... what am I doing wrong?