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prove that the curves 2y 2 = x 3 and y 2 = 32x cut each other orthogonally at the origin.

prove that the curves 2y2 = x3 and 
y2= 32x cut each other orthogonally at the origin. 

Grade:12

1 Answers

Vikas TU
14149 Points
4 years ago
Find out their slopes .
4y.dy/dx = 3x^2
(dy/dx)1 = 3x^2/4y............(1)
 
and
2y.dy/dx = 32
(dy/dx)2 = 16/y...............(2)
m1 * m2  = > -1
check l.hs.
3x^2/4y * 16/y = > 12x^2/y^2 put y^2 = 32x
=> 12x^2/32x =  > 3x/8 at x = 0 product is zero.

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