#### Question

Prove that the curves *x* = *y*^{2} and *xy = k* cut at right angles if 8*k*^{2} = 1. [**Hint**: Two curves intersect at right angle if the tangents to the curves at the point of intersection are perpendicular to each other.]

#### Solution

The equations of the given curves are given as `x = y^2 and xy = k`

Putting *x* = *y*^{2} in *xy* = *k*, we get:

This implies that we should have the product of the tangents as − 1.

Thus, the given two curves cut at right angles if the product of the slopes of their respective tangents at

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Solution Prove that the Curves X = Y2 and Xy = K Cut at Right Angles If 8k2 = 1. [Hint: Two Curves Intersect at Right Angle If the Tangents to the Curves at the Point of Intersection Are Perpendicular to Each Other.] Concept: Tangents and Normals.