Q. 23

# Prove that the curves x = y2 and xy = k cut at right angles* if 8k2 = 1.

It is given that the curves x = y2 and xy = k

Now, putting the value of x in y = k, we get

y3 = k

Then, the point of intersection of the given curves is

On differentiating x = y2 with respect to x, we get

Then, the slope of the tangent at xy = k at

is

As we know that two curves intersect at right angles if the tangents to the curve at the point of intersection are perpendicular to each other.

So, we should have the product of the tangent as -1.

Then, the given two curves cut at right angles if the product of the slopes of their respective tangent at is -1.

Cubing both side, we get

8k2 = 1

Therefore, the given two curves cut at right angles if 8k2 = 1.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
How to find Maxima & Minima?43 mins
Practise Questions - Application of Derivatives45 mins
Interactive quizz on tangent and normal, maxima and minima43 mins
Interactive quiz on maxima and minima48 mins
Tangent & Normal To A Curve53 mins
Test your knowledge of Tangents & Normals (Quiz)52 mins
Tangents & Normals (Concept Builder Class)55 mins
Application of Biotechnology48 mins
Application of Nerst Equation20 mins
Application of Biotechnology | Concepts - 0256 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses