Find the radius of the largest circle with centre
(1,0) that can be inscribed in the ellipse $$x ^{2}/16 + y ^{2}/4 = 1$$

Question

Find the radius of the largest circle with centre 
(1,0) that can be inscribed in the ellipse $$x ^{2}/16  + y ^{2}/4  = 1$$

anonymous · Answer

2? If I'm imagining it right

anonymous · Answer

sorry, @Ishaan, thats not the answer

anonymous · Answer

Oh, Circle's center (1,0) I took it as (0,0)

anonymous · Answer

$$(x-1)^2 + y^2 = r^2$$$$x^2 -2x + 1 +y^2 = r^2$$$$x^2 - 2x + y^2 =r^2 -1$$Hmm how about sqrt(5)?

anonymous · Answer

answer:
$$\sqrt{11}/3$$
wanna know the process..

anonymous · Answer

No :/ I will have to solve it now. I got the answer but had to use Calculus, do you know of a better way, something graphical?

anonymous · Answer

or Geometrical?

experimentx · Answer

well, i think it can be done this way,

the maximum radius of the circle will the the smallest distance from the center of circle to the curve.

now our point is (1,0), let x, y be the point in the ellipse.

the distance is d = sqrt{(x-1)^2 + y^2} --> if we change this y into x's then we will have a function a function in x, minimizing the value taking extremum might give us this point x, and so we might find corresponding y, hence the radius of the circle.

anonymous · Answer

I did the same

experimentx · Answer

best of luck isshan ... i hope you will share the result with me.

anonymous · Answer

Thanks experimentx! I did fine today.