Solution to Problem 267

Correct solutions came from Vincent Lynch, UK; Bill Webb, USA; David Stigant, USA; John Snyder, USA. 

Let L be one such tangent line with y-intercept (0, y_L) and x-intercept (x_L, 0).  The slope of L is (y_L - 0)/(0 - x_L) = (y_L - 0)/(0 - ay_L) = -1/a, as long as (x_L, y_L) ≠ (0,0); therefore the slope of the tangent line is independent of the point, giving us the equation dy/dx = -1/a, y = (-1/a)x + c, for arbitrary constant c.  In the exceptional case, the x-intercept and y-intercept of every tangent line are zero so y = mx, for any constant m.

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