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Assume that when the plane curve C shown in the figure is revolved about the x axis, it generates a surface with the property that all light rays L parallel to the x axis striking the surface at a point P(x,y) are reflected to a single point O (the origin). Use the fact that the angle of incidence is equal to the angle of reflection to determine a differential equation that describes the shape of the curve C.

My work:

The tangent of angle that the tangent line makes with the x axis is the slope of that tangent line, dy/dx. Using some simple trig, I was able to determine that angle phi = 2theta, so its supplementary angle is 180-2theta. Therefore the angle that the tangent makes with the x axis is theta. The distance between the origin is sqrt(x^2+y^2), and this is an isoceles triangle, so the distance between the origin and where the tangent line intersects the x axis is also sqrt(x^2+y^2). Drawing a right triangle to find out what the tangent of theta is, I have a triangle with legs length sqrt(x^2+y^2)-x and y

So I came up with tan theta = dy/dx = y/(sqrt(x^2+y^2)-x). Why does my book say that the answer is (sqrt(x^2+y^2)-x)/y?

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# Quick question-Representing a curve w/a DE

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