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

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

Grade:11

2 Answers

Badiuddin askIITians.ismu Expert
148 Points
14 years ago

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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Shikhar Batham
15 Points
5 years ago
(x-1)^2+y^2=a^2
a is radius of that circle 
Let a point on ellipse ( a Cos© , b Sin ©) 
Find out distance of this point from (1,0) and put on place of a^2  
You will have aproxa answer
 

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