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Question-197730




Question Number 197730 by ajfour last updated on 27/Sep/23
Commented by ajfour last updated on 27/Sep/23
Determine r in terms of a,b.
Determinerintermsofa,b.
Commented by ajfour last updated on 27/Sep/23
https://youtu.be/0sSIzDZtOBQ?si=jQAFPvy744djWIga
Commented by ajfour last updated on 27/Sep/23
My lecture on You tube   Differentiation : Lesson 2
MylectureonYoutubeDifferentiation:Lesson2
Answered by mr W last updated on 27/Sep/23
(h−r)^2 +k^2 =r^2   ⇒k^2 =r^2 −(h−r)^2 =h(2r−h)  (h/a^2 )+(k/b^2 )×(−((h−r)/k))=0  ⇒h=((a^2 r)/(a^2 −b^2 ))=(r/(1−μ^2 )) with μ=(b/a)  (h^2 /a^2 )+(k^2 /b^2 )=1  (h^2 /a^2 )+((h(2r−h))/b^2 )=1  let λ=(r/a)  (λ^2 /((1−μ^2 )^2 ))+((λ^2 (2−(1/(1−μ^2 ))))/(μ^2 (1−μ^2 )))=1  ⇒λ=μ(√(1−μ^2 ))  ⇒r=b(√(1−(b^2 /a^2 )))  ✓
(hr)2+k2=r2k2=r2(hr)2=h(2rh)ha2+kb2×(hrk)=0h=a2ra2b2=r1μ2withμ=bah2a2+k2b2=1h2a2+h(2rh)b2=1letλ=raλ2(1μ2)2+λ2(211μ2)μ2(1μ2)=1λ=μ1μ2r=b1b2a2
Commented by mr W last updated on 27/Sep/23
Commented by ajfour last updated on 27/Sep/23
Yes sir. Thank you.
Answered by ajfour last updated on 27/Sep/23
(x−r)^2 +y^2 =r^2   (x^2 /a^2 )+(y^2 /b^2 )=1  ⇒   (((x−r)^2 )/b^2 )+1−(x^2 /a^2 )=(r^2 /b^2 )  multiplying by a^2 b^2   (a^2 −b^2 )x^2 −(2ra^2 )x+a^2 b^2 =0  D=0  4r^2 a^4 =4a^2 b^2 (a^2 −b^2 )  r=((b/a))(√(a^2 −b^2 ))
(xr)2+y2=r2x2a2+y2b2=1(xr)2b2+1x2a2=r2b2multiplyingbya2b2(a2b2)x2(2ra2)x+a2b2=0D=04r2a4=4a2b2(a2b2)r=(ba)a2b2
Commented by mr W last updated on 27/Sep/23
very nice approach!
veryniceapproach!

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