43som1 help in dese.....
1)If α and β are ends of a focal chord of an ellipse of eccentricity e, find tan(α/2).tanβ(/2)
2)Normals drawn to ellipse x2a2 + y2b2=1 at P meet the coordinate axes at A, B. Find the locus of mid point of A and B.
3)A tangent drawn to x2a2+y2b2=1 at P is such that it intersects the auxiliary circle at A and B. If S and S' are foci, then find min value of S'A + SB
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3 Answers
1357(ae,0);(acosα,bsinα);(acosβ,bsinβ)
y-bsinαx-acosα=bsinβ-bsinαacosβ-acosα
-bsinαae-acosα=bsinβ-bsinαacosβ-acosα
-sinαe-cosα=sinβ-sinαcosβ-cosα
e=sin(α-β)/(sinα-sinβ)
proceed from here
1357for second
take P as (acosθ,bsinθ)
find the equation of normal,
find the points A and B
get the locus