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: 10
        
If PQ is the double ordinate of the parabola y2=4ax then what is the locus of its point of trisection?
2 years ago

Answers : (2)

Arun
23382 Points
							
Dear Vijaya
 
The equation y^2 = 4ax can be parametrised as: 
x = at^2, y = 2at. 

If the extremities of the double ordinate are (at^2, 2at) and (at^2, - 2at), then its points of trisection have ordinates y1 and y2 where: 
y1 = - 2at + 4at / 3 = 2at / 3 
y2 = - 2at + 8at / 3 = - 2at / 3 

For both of these points: 
y^2 = 4a^2 t^2 / 9 
y^2 = (4a / 9)(at^2) 
y^2 = 4(a / 9)x. 

The locus is the parabola y^2 = 4bx where: 
b = a / 9.
hence locus -
y^2 = (4/9) ax
 
Regards
Arun(askIITians forum expert)
2 years ago
Harsh Vardhan
13 Points
							
Let the extremities of double ordinate be (k,l) and (k,-l)
Let P(x1,y1) be any point on the double ordinate which divides the line in the ratio 1:2
 
P(x1,y1)=1(k)+2(k)/1+2,1(-1)+2(l)/1+2
=(K,l/3)
Here x1=k y1=l/3,l=3y1
(K,l)=(x1,3y1)
As (k,l) lies on the parabola
L^2=4ak
(3y1)^2=4ax1
9y1^2=4ax1
Hence the locus of the point of trisection is 
9y^2=4ax
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

  • 53 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