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

                        

A line L drawn from pt. p(4,3) to meet the line L1:3x+4y+5=0,,,,and L2: 3x+4y+15=0.....at points A and B respectively .From point A a line perpendicular to L is drawn meeting the lines L2 at A1.Similarly from pt. P line perpendicular toL is drawn meeting the line L1 at B1.Thus a llgram AA1BB1 is completed.Find the equation of L so that area of the llgram is least?

11 years ago

Answers : (1)

Ramesh V
70 Points
							

AA1BB1 is a parallogram with 2 equal triangles AA1B and ABB1

Let AB=b

perpendicular distance btn L1 & L2 lines is p=2 units

Now consider traingle ABB1 ( from simple trigonometry )

we have its area = b2p / 2*(b2 - p2)1/2

for PA=r1 and PB=r2 and let  tan X be slope of line L

In polar coordinate form :

A ( 4+r1cos X , 3+r1sin X )   and B ( 4+r2cos X , 3+r2sin X )

on substituting A and B in L1 and L2 , we have

r1=|-29| / (3 cos X + 4 sin X)    and

r2=|-39| / (3 cos X + 4 sin X)

So AB= |r2 - r1|

AB = b =10 / (3 cos X + 4 sin X)

            b = 2 / sin (X+k)               :  where k=sin-1(3/5)

So total area is twice area of traingle ABB1

Area = b2p / (b2 - p2)1/2

          = 4 / sin (X+k)*cos (X+k)

          = 4 / sin 2(X+k)

For area to min. = sin 2(X+k) = 1

or                            2(X+k) = Pi /2

                               X = Pi/4 - k

     tan X = (1 - tan k)/(1+ tan k)

                = (1 -0.75)/(1+ 0.75) 

slope of L is : tan X = 1/7

So eqn. L is : x -7y+17 = 0


11 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

  • 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