# Check the orthogonality of the curves $$y^2$$ = x and $$x^2$$ = y.

## Solution :

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

At (1, 1) for first curve $$2y({dy\over dx})_1$$ = 1  $$\implies$$  $$m_1$$ = $$1\over 2$$

& for second curve 2x = $$({dy\over dx})_2$$ $$\implies$$  $$m_2$$ = 2

$$m_1m_2$$ = -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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