Find the radius of curvature of the parabola y^2 = 4px at (0,0).

Please teach me how to solve this question. Thank you very much.

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- February 8th 2007, 08:05 AMJenny20radius of curvature
Find the radius of curvature of the parabola y^2 = 4px at (0,0).

Please teach me how to solve this question. Thank you very much. - February 8th 2007, 12:07 PMJenny20
Please check my work. The answer of this question is 2 lpl.

I got the answer is 2p. Could you please help me find out the reason? Thank you very much. - February 8th 2007, 12:07 PMCaptainBlack
In this case take the curvature as:

where we consider as a function of and differentiation is with respect to

This has and interchanged compared to the usual expression but the absolute value of the curvature is the same either way, and this way is easier to handle.

Here:

so:

,

and:

so at , , so:

so the radius of curvature .

RonL