An ellipse is drawn with major axis and minor axis of lengths 10 and 8 respectively. Using one focus as the centre,a circle is drawn that is tangent to the ellipse,with no part being outside the ellipse. Then the radius of the circle is: Ans : Radius = 2 HOW???
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Since $$a = \frac{10}{2} = 5, b = \frac{8}{2} = 4$$ Then, to find the focii $$c^2 = a^2 - b^2 = 25 - 16 = 9$$ So that $c = 3$. Therefore if we want to draw a circle tangent to the ellipse, with no part being outside the ellipse we still have 2 units inside the ellipse (since $a - c = 5 - 3 = 2$). Hence using one focus as the center, a circle is drawn that is tangent to the ellipse, with no part being outside the ellipse.
Ahmed
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