badge image

Enroll For Free Now & Improve Your Performance.

×
User Icon
User Icon
User Icon
User Icon
User Icon

Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping
Menu
Grade: 12

                        

Prove that the curves y 2 = 4x and x 2 + y 2 – 6x + 1 = 0 touch each other at the point (1, 2).

2 months ago

Answers : (1)

Anand Kumar Pandey
askIITians Faculty
2803 Points
							Dear Student

It is given that
curve equations are:y^2= 4x....(1)
and
x^2+y^2–6x+ 1 = 0..... (2)
differentiating (i) w.r.t. x, we get

2y.(dy/dx) = 4
⇒dy/dx = 2/y
Slope of tangent at (1, 2),
m1= 2/2 = 1
Differentiating (ii) w.r.t. x, we get

2x + 2y.(dy/dx)–6 = 0
2y. dy/dx = 6–2x
⇒dy/dx = (6–2x)/ 2y
Hence, the slope of the tangent at the same point (1, 2)
⇒m2= (6–2 x 1)/ (2 x 2) = 4/4 = 1
It can be seen that
m1= m2= 1 at the point (1, 2).
Thus, the given circles touch each other at the same point (1, 2).


Thanks
2 months ago
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies


Course Features

  • 731 Video Lectures
  • Revision Notes
  • Previous Year Papers
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Test paper with Video Solution


Course Features

  • 51 Video Lectures
  • Revision Notes
  • Test paper with Video Solution
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Previous Year Exam Questions


Ask Experts

Have any Question? Ask Experts

Post Question

 
 
Answer ‘n’ Earn
Attractive Gift
Vouchers
To Win!!! Click Here for details