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Prove that the curves 2y2 = x3, y = 32x cut each other at right angle at the origin. |
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Answer» Curves are 2y2 = x3 ...(1) and y = 32x ...(2) 4y(dy/dx) = 3x2 (dy/dx) = 3x2/4y ...(3) and (dy/dx) = 32 ...(4) Angles of the curves at Point (0,0) From (4), (dy/dx) at (0,0) = 32 From (3), (dy/dx) th (0,0) = 0 So, angle of both the curves at (0,0) = |90° - 0°| = 90° proved |
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