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show that the follwoing curve intersect orthogonally at the indicated points x^2 = 4y and 4y + x^2 = 8 at (2,1)

show that the follwoing curve intersect orthogonally at the indicated points 
x^2 = 4y and 4y + x^2 = 8 at (2,1)

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/4 = x/2 = 1
(dy/dx)2 = -2x/4 = -x/2 = -1
clearly product of slope is -1 hence curve intersect orthogonally.

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