determine the slope of a point on a ellipse

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the equation of ellipse is

$Ax^2 + By^2 + Cx + Dy + Exy + F = 0$

for slope,

$2Ax+2By*dy/dx+C+D*dy/dx+Ex*dy/dx+Ey=0$

so, $(2By+D+Ex)*dy/dx=-(2Ax+C+Ey)$

=> $dy/dx=-(2Ax+C+Ey)/(2By+D+Ex)$

This should be the equation of slope at any point on a ellipse. But I found different equation from the following link

The values of dx and dy are calculated from:

dx = 2Ax + C + Ey
dy = 2By + D + Ex

The gradient/slope is calculated from:

 dy 2By + D + Ex
M = -- = ------------ dx 2Ax + C + Ey

()

My question is which one is correct?

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1 Answer

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Your result is correct.

In the reference the slope of normal has been given by mistake.

Take the simplest case of a circle setting all else to zero except $A,B$.

By differentiating wrt x: $ A x + B y y^ \prime = 0, $ that you gave.

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