Q. 23

# Prove that the cu

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.
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 RELATED QUESTIONS :

Find the equationRD Sharma - Volume 1

Find the equationMathematics - Board Papers

Find the equationRD Sharma - Volume 1

Find the equationRD Sharma - Volume 1

Find the equationRD Sharma - Volume 1

Find the equationRD Sharma - Volume 1

Find the conditioMathematics - Exemplar

Find the equationMathematics - Board Papers