If ax^2 +2hxy+by^2 +2gx + 2fy+c=0 & ax^2 + 2hxy + by^2 -2gx - 2fy +c=0 each represents pair of straight lines. Prove that the area of parallelogram enclosed by them is (2|c|)/((h^2 -ab) ^(1/2))

Question

Vikas TU · Answer

Dear Student,

ax2+2hxy+by2+2gx+2fy+c=0 is a couple of straight lines. It must be of the frame (lx+my+n)(px+qy+r)=0, where a=lp, h=12(lq+mp), b=mq, ..., c=nr (on looking at coefficients). Thus ax2+2hxy+by2−2gx−2fy+c=0 is then given by (lx+my−n)(px+qy−r)=0.

Discriminant Δ = stomach muscle – h2 = - (lq – mp)2/4.

The line lx+my+n=0 meets the lines px+qy±r=0 at the focuses (±(mr – nq)/(lq – mp), ±(lr – np)/(lq – mp)). The separation between two focuses = 2r √(l2 + m2)/(lq – mp) = Length of the side of the parallelogram = l1.

The opposite separation between the parallel lines lx+my±n=0 = 2n/√(l2 + m2) = Distance between inverse sides of the parallelogram = l2.

In this way territory = l1l2 = |2nr/(1/2 x (lq – mp))| = 2|c|/√(- Δ).

Cheers!!

Regards,

Vikas (B. Tech. 4^th year
Thapar University)

Supriya Bhowmik · Answer

show that one of the bisectors of the angles between the pair of lines ax^ overline 2 +2hxy+by^ 2 =0 will pass through the point of intersection of two lines a * x ^ 2 + 2hxy + b * y ^ 2 + 2gx + 2fy + c = 0 ifh(g ^ 2 - f ^ 2) = fg(a - b)

Thank you for registering.

Register Now and Win Upto 25% Scholorship for a Full Academic Year !

Enter Your Details

Registration done!

Guest

If ax^2 +2hxy+by^2 +2gx + 2fy+c=0 & ax^2 + 2hxy + by^2 -2gx - 2fy +c=0 each represents pair of straight lines. Prove that the area of parallelogram enclosed by them is (2|c|)/((h^2 -ab) ^(1/2))

If ax^2 +2hxy+by^2 +2gx + 2fy+c=0 & ax^2 + 2hxy + by^2 -2gx - 2fy +c=0 each represents pair of straight lines. Prove that the area of parallelogram enclosed by them is (2|c|)/((h^2 -ab) ^(1/2))

2 Answers

Think You Can Provide A Better Answer ?

Other Related Questions on Analytical Geometry

ASK QUESTION

Answer and earn gift vouchers

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Complete Self Study Package designed by Industry Leading Experts

Live 1-1 coding classes to unleash the Creator in your Child

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Register Now & Win Upto 25% Scholorship

Thank you for registering.

Register Now and Win Upto 25% Scholorship for a Full Academic Year !

Enter Your Details

Registration done!

Guest

IIT JEE Courses

One Year IIT Programme

Two Year IIT Programme

Crash Course

NEET Courses

One Year NEET Programme

Two Year NEET Programme

One to One

School Board

Live Online classes

Class 11 & 12

Class 9 & 10

Class 6, 7 & 8

Test Series

JEE test series

NEET test series

C.B.S.E test series

Complete Self Study Packages

FULL COURSE

For class 12th

For class 11th

If ax^2 +2hxy+by^2 +2gx + 2fy+c=0 & ax^2 + 2hxy + by^2 -2gx - 2fy +c=0 each represents pair of straight lines. Prove that the area of parallelogram enclosed by them is (2|c|)/((h^2 -ab) ^(1/2))

If ax^2 +2hxy+by^2 +2gx + 2fy+c=0 & ax^2 + 2hxy + by^2 -2gx - 2fy +c=0 each represents pair of straight lines. Prove that the area of parallelogram enclosed by them is (2|c|)/((h^2 -ab) ^(1/2))

2 Answers

Think You Can Provide A Better Answer ?

Other Related Questions on Analytical Geometry

ASK QUESTION

Answer and earn gift vouchers

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Complete Self Study Package designed by Industry Leading Experts

Live 1-1 coding classes to unleash the Creator in your Child

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Register Now & Win Upto 25% Scholorship