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: 11
        
two equal parabolas have the same focus & their axis at right angles, a normal to one is perpendicular to the normal to the other.Prove that the locus of the intersection of these normals is another parabola
one year ago

Answers : (1)

Arun
22972 Points
							
 

The equation of the normal to the parabola y2 = 4ax is y = mx – 2am – am3.

It passes through the point (h, k) if 

k = mh – 2am – am3 => am3 + m(2a – h) + k = 0. … (1)

Let the roots of the above equation be m1, m2and m3. Let the perpendicular normals correspond to the values of m1 and m2 so that m1m2 = –1.

From equation (1), m1 m2 m3 = -k/a. Since m1 m2 = –1, m3 = k/a.

Since m3 is a root of (1), we have a (k/a)3+k/a (2a – h) + k = 0. ⇒ k2 + a(2a – h) + a2 = 0

⇒ k2 = a(h – 3a).

Hence the locus of (h, k) is y2 = a(x – 3a).

one year 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

  • 731 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