Solution:
Given curve constrained by point acos θ , bsin θ
Now x=acosθ;y=bsinθ⇒xa=cosθ,yb=sinθ⇒xa2+yb2=1 This is equation of ellipse
Now at point θ
(x1,y1)=(acosθ,bsinθ)
Hence the equation of the tangent
a2acosθ1x+b2bsinθ1y=1axcosθ1x+bysinθ1=1
Now the equation of tangent at point θ;θ1+2π
(acosθ,bsinθ)=(acos(θ1+2π),bsin(θ1+2π))=(−asinθ1,bcosθ1)
Now equation of tangent
−axsinθ1+bycosθ1=1
The intersection point of both tangents
x=(1−businθ)cosθ1a−asinθ1(1−businθ)cosθ1a+bycosθ1=1y=b(sinθ1+cosθ1)Similarlyx=a(cosθ1−sinθ1)
Hence intersection point
x=a(cosθ1−sinθ1)y=b(sinθ1+cosθ1)
Locus of intersection point
a2x2+b2y2=2
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