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TANGENTS AND NORMALS show that the following curve intersect orthogonally at the indicated points x^2=y and x^3 + 6y = 7 at (1,1)

TANGENTS AND NORMALS
 
show that the following curve intersect orthogonally at the indicated points 
x^2=y and x^3 + 6y = 7 at (1,1)

Grade:12

1 Answers

Sunil Raikwar
askIITians Faculty 45 Points
6 years ago

We know that the two curve intersect orthogonally if angle between their tangents at the point of intersection is 90 degree & two tangents are perpendicular if product of their slope is -1.
(dy/dx)1 = 2x = 2
(dy/dx)2 = -3x2/6 = -1/2
Clearlly product of slope is -1 hence given curve intersect orthogonally.

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