find radius of largest circle with centre (1,0)which can be inscribed in ellipse x^2 + 4y^2 =16

Dear tushar

 x^2 + 4y^2 =16

point on the parabola(acosθ,bsinθ)=(4cosθ,2sinθ)

equation of normal of parabola

    axsecθ -bycosecθ =a² -b²

 or 4 xsecθ - 2y cosecθ =12

it passes through (1,0)

 so secθ =3

  or cos θ =1/3

   sinθ =2 √2/3

 so point become (4cosθ,2sinθ)=(4/3,4 √2/3)

now find the distance between point (1,0) and (4/3,4 √2/3)  it will be radius  of circle.

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