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

                        

If x cos a + y sin a = p touches the cuve x^m .y^n = a^(m+n) ;prove that p^(m+n) . m . n = (m+n)^(m+n) cos^m a sin^n a

4 years ago

Answers : (1)

Nishant Vora
IIT Patna
askIITians Faculty
2467 Points
							Simplify algebra by making subs X=x/a, Y=y/b and m=n/(n-1)

Xᵐ + Yᵐ = 1 … (i)

Xacotα + Yb = pcosecα … (ii)

Diff (i) wrt X : mXᵐ⁻¹ + mYᵐ⁻¹(dY/dX) = 0 ⟹ dY/dX = −(X/Y)ᵐ⁻¹

At pt of contact (X,Y) have grad (i) = grad (ii) so −acotα/b=−(X/Y)ᵐ⁻¹ … (iii)

Sub in (ii) for acotα : bXᵐ/Yᵐ⁻¹ + Yb = pcosecα ⟹ b(Xᵐ+Yᵐ) = pYᵐ⁻¹cosecα ⟹ Yᵐ⁻¹ = (b/p)sinα

Also using (iii), Xᵐ⁻¹ = (a/p)cosα

Sub in (i) for X,Y and adjust to get (acosα/p)^(m/(m-1)) + (bsinα/p)^(m/(m-1)) = 1

Setting m/(m-1)=n and multiply by pⁿ gives desired result
3 years 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