Ellipse & Circle characteristics: Selected 5 practice questions Level 3 (details in description)

Ellipse & Circle characteristics: Selected 5 practice questions Level 3 (details in description)
Example 1: An ellipse is drawn with major and minor axis of lengths 10 and 8. Using one focus as a center, a circle is drawn which is tangent to the ellipse, with no part of circle outside of ellipse, find the radius?
Example 2: Consider an ellipse and concentric circle. The circle passes through focii of the ellipse in four distinct point. If length of major axis is 15, area of triangle PS1S2 is 26. Find eccentricity of the ellipse?
Example 3: If the circle (x-2)^2+(y+3)^2=16 touching the ellipse (x-2)^2/p^2+(y+3)^2/q^2=1 from inside. If (2,-6) is one of the focus, find (p.q)?
Example 4: A line passing through end of major and minor axis of ellipse x^2+9y^2=9, meets the auxillary circle at the point M. Find area of triangle OAM?
Example 5: Equation of the largest circle with center (1,0) that can be inscribed in the ellipse x^2+4y^2=16? Support the channel:

[iitianranker]

sir in the example 3 ans should be option 1 as focus is of the form ( 0, + - ae) hence tem below (y+3)^2 that is q should be greater

[krishnabharadwaj]

i had doubts in exactly thses type of questions of circle touching ellipse and sir solved them 👍

[virajchandra]

Sir for radius equals to 2 the circle won't it be outside of the ellipse?