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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
10 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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