Check the orthogonality of the curves y2 = x and x2 = y.

Solution :

Solving the curves simultaneously we get points of intersection as (1, 1) and (0, 0).

At (1, 1) for first curve 2y(dydx)1 = 1    m1 = 12

& for second curve 2x = (dydx)2   m2 = 2

m1m2 = -1 at (1, 1).

But at (0, 0) clearly x-axis & y-axis are their respective tangents hence they are orthogonal at (0, 0) but not at (1, 1). Hence these curves are not said to be orthogonal.


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