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    What is the radius of curvature formula for an ellipse at slope = 1?

    The formula for an ellipse is x^2/a^2+y^2/b^2=1. The formula for the slope of an ellipse is y'(x)= - (x/a^2)/(y/b^2). Setting y'(x)=1, we have (x/a^2)/(y/b^2)=-1. Solving these two equations yields the solutions: x = - a^2/sqrt(a^2+b^2), y= +b^2/sqrt(a^2+b^2), and x = +a^2/sqrt(a^2+b^2), y= -...
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