Question

20. The radius of curvature of the catenary y = c tan y is
21.At (0,0) the radius of curvature of the circle x² + y2 - 2x - 2y = 0 is​

Answer 1

Answer:

Equation of the curve is y = c cos h x/c                                                                              (1) ∴  dy/dx = y1 = sin h x/c                                                             (2) and dy1/dx = y2 = (1/c) cos h (x/c)                                               (3) thus p =                                                              (4) Now portion of the normal intercepted between the curve and the X-axis is                                                                        (5) Clearly from eqn (4) and (5) we see that ρ (radius of curvature) = n (length of the normal) = c cos h2 x/c = y2/c                        

Explanation:

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