An ellipse is drawn with the major axis and latus rectum of length 10 and 
, respectively. Using one focus as centre, a circle is drawn that is touch to the ellipse, with no part of the circle being outside the ellipse, then the radius of circle is
Text Solution
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Given, length of major axis 
and length of latus rectum 
Therefore, the equation of ellipse is
Then, foci are 
Now, the circle having centre 
is
On eliminating 
from Eqs. (i) and (ii), we get
Since, the circle touch the ellipse, the above equation has equal roots.
Hence, 
i.e. 
,
which is not possible.
Then, the circle will touch the ellipse at the end of the major axis 
.
Hence, the radius is 2 .
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