& 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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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