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: 12th pass

                        

Show that the locus of a point that divides a chord of slope 2 of a parabola y^2=4x internally in the ratio 1: 2 is a parabola. Find the vertex of the parabola.

6 years ago

Answers : (2)

mycroft holmes
272 Points
							Consider P(x) = (x-2)^2+(x-3)^2

This is the sum of two quadratics with real roots.

But this quadratic is always positive and has no real roots.
						
6 years ago
noogler
489 Points
							
Let the two points on the given parabola be (t12, 2t1) and (t22, 2t2). Slope of the line joining these points is 
2=[2t2-2t1]/[t22-t12]=2/t1+t2

=> t1 + t2 = 1 

Hence the two points become (t12 , 2t1) and ((1 − t1)2 , 2(1 − t1))

Let (h , k) be the point which divides these points in the ratio 1 : 2
h=(1-t1)2+2t1/3=1-2t1+3t12/3       ....(1)
 

k=[2(1-t1)+4t1]/3=2+2t1/3               ....(2)
 

Eliminating t1 from (1) and (2), we find that 4h = 9k2 − 16k + 8 

Hence locus of (h , k) is 

(y-8/9)2=4/9(x-2/9)

This is a parabola with vertex (2/9 , 8/9)
 
 
 
HOPE U UNDERSTOOD
APPROVE IF IT HELPED U
5 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

  • 101 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