The radius of curvature rho of the ellipse dfrac x^2 a^2 +dfrac y^2 b^2 =1 at the end of the minor axis (0,b) is:

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SSC Applied Mathematics QUESTION #1323

Question 1

The radius of curvature \(\rho\) of the ellipse \(\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1\) at the end of the minor axis \((0,b)\) is:

\(\dfrac{b^2}{a}\)
\(\dfrac{a^2}{b}\)✔️
\(\dfrac{a}{b}\)
\(\dfrac{b}{a}\)

Correct Answer Explanation

The radius of curvature of an ellipse at \((0,b)\) (end of minor axis): using the formula \(\rho=\dfrac{(a^2\sin^2t+b^2\cos^2t)^{3/2}}{ab}\) at \(t=\pi/2\): \(\rho=\dfrac{(a^2)^{3/2}}{ab}=\dfrac{a^3}{ab}=\dfrac{a^2}{b}\).

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