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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.] - CBSE (Commerce) Class 12 - Mathematics

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Question

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.]

Solution

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

Putting x = y2 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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APPEARS IN

 NCERT Solution for Mathematics Textbook for Class 12 (2018 to Current)
Chapter 6: Application of Derivatives
Q: 23 | Page no. 213
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.
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