1.

Prove that the curves 2y2 = x3, y = 32x cut each other at right angle at the origin.

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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