Take Class 12 Tuition from the Best Tutors
Affordable fees 1-1 or Group class Flexible Timings Verified Tutors Search in
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.]
Asked by Srinitha Last Modified
Answer 
Harshit Bhardwaj
The equations of the given curves are given as
Putting x = y2 in xy = k, we get:
Thus, the point of intersection of the given curves is
.
Differentiating x = y2 with respect to x, we have:
Therefore, the slope of the tangent to the curve x = y2 atis 
On differentiating xy = k with respect to x, we have:
∴ Slope of the tangent to the curve xy = katis given by,
We know that two curves intersect at right angles if the tangents to the curves at the point of intersection i.e., at are perpendicular to each other.
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 is −1.
Hence, the given two curves cut at right angels if 8k2 = 1.
read less
Sherine Das
Well Qualified and Certified Mathematics B.Ed(M.G Usty)Teacher with more than13 years of Experience
Sherine Das
Well Qualified and Certified Mathematics B.Ed(M.G Usty)Teacher with more than13 years of Experience
View 1 more Answers
Related Questions
Find the equations of the tangent and normal to the parabola y2 = 4ax at the point (at2, 2at).
Find the slope of the normal to the curve x = 1 − a sin θ, y = b cos2θ at
.
Find the slope of the tangent to the curve y = 3x4 − 4x at x = 4.
Now ask question in any of the 1000+ Categories, and get Answers from Tutors and Trainers on UrbanPro.com
Ask a QuestionRecommended Articles
Meet Radhe Shyam Burman, an MBA Tutor from...
Radhe Shyam is a highly skilled accounts and finance trainer with 8 years of experience in teaching. Accounting is challenging for many students and that’s where Radhe Shyam’s expertise comes into play. He helps his students not only in understanding the subject but also advises them on how to overcome the fear of accounts...
Read full article >
Meet Sandhya R, a B.Sc tutor from Bangalore
Sandhya is a proactive educationalist. She conducts classes for CBSE, PUC, ICSE, I.B. and IGCSE. Having a 6-year experience in teaching, she connects with her students and provides tutoring as per their understanding. She mentors her students personally and strives them to achieve their goals with ease. Being an enthusiastic...
Read full article >
Meet Swati, a Hindi Tutor from Bangalore
Swati is a renowned Hindi tutor with 7 years of experience in teaching. She conducts classes for various students ranging from class 6- class 12 and also BA students. Having pursued her education at Madras University where she did her Masters in Hindi, Swati knows her way around students. She believes that each student...
Read full article >
Meet Urmila, an MBBS tutor from Bangalore
Urmila is a passionate teacher with over 8 years of experience in teaching. She is currently pursuing her Ph. D. She provides classes for Class 11, Class 12, MBBS and Medical tuition. Urmila began her career in teaching long before she became a teacher. She used to provide classes for foreign national students in her college...
Read full article >
Looking for Class 12 Tuition ?
Learn from the Best Tutors on UrbanPro
Are you a Tutor or Training Institute?
Join UrbanPro Today to find students near youThe best tutors for Class 12 Tuition Classes are on UrbanPro
The best Tutors for Class 12 Tuition Classes are on UrbanPro
5
