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& equation of ellipse is, 2²745²2=4 x² + y² = 1 1² 2²=4₁ 6=1 we know, two diameters Y=m₁ x and y=m₂x are conjugate iff. 2 mim₂ = - a² given equation of diameter is, зи-у=0) Y= зн _'~ m₁ = 3 -. by Ⓡ, (3) m₂ = = +₁ + m₂ = 7/₂ - :. rerd erum of conjugate diameter is, y=-=22x AN 12y=-x x+12y=0 An

& equation of ellipse is, 2²745²2=4 x² + y² = 1 1² 2²=4₁ 6=1 we know, two diameters Y=m₁ x and y=m₂x are conjugate iff. 2 mim₂ = - a² given equation of diameter is, зи-у=0) Y= зн _'~ m₁ = 3 -. by Ⓡ, (3) m₂ = = +₁ + m₂ = 7/₂ - :. rerd erum of conjugate diameter is, y=-=22x AN 12y=-x x+12y=0 An

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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& equation of ellipse is, 21 ²745²2= 4 2 22²2 +4²=1 1² 2²=4₁ 6==1 we know, two diameters Y = m₁ x and y=m₂x are conjugate iff. 2 mim --6-- (*))) 9² given equation of diameter is, 32-y=07) Y= 3x -'~ m₁ = 3 2. by Ⓡ, (3) m₂ = = =+ + m₂ = 7₂ : red equier of conjugate diameter is, y = 7/22x 12y=-x x+12y=0 Am
Transcribed Image Text:& equation of ellipse is, 21 ²745²2= 4 2 22²2 +4²=1 1² 2²=4₁ 6==1 we know, two diameters Y = m₁ x and y=m₂x are conjugate iff. 2 mim --6-- (*))) 9² given equation of diameter is, 32-y=07) Y= 3x -'~ m₁ = 3 2. by Ⓡ, (3) m₂ = = =+ + m₂ = 7₂ : red equier of conjugate diameter is, y = 7/22x 12y=-x x+12y=0 Am
Expert Solution
Step 1

Equation of the ellipse is 

     x2 + 4y2 = 4

    => x2/4 + y2/1 = 1

    => a2 = 4 and b2 = 1 [here, the obtained equation is compared with the standard form x2/a2 + y2/b2 = 1]

We know, two diameters y = m1x and y = m2x are conjugate iff  

      m1m2 = -b2/a2 . . . . . (*) 

Given equation of diameter is

     3x - y = 0 => h = 3x

       => m1 = 3

      So, (3)m2 = -1/4

           => m2 = -1/12 

   

 

 

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