An ellipse is drawn with major and minor axes | vedclass

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(B) Given $2a = 10 \Rightarrow a = 5$ and $2b = 8 \Rightarrow b = 4$. The eccentricity $e$ is given by $e^2 = 1 - \frac{b^2}{a^2} = 1 - \frac{16}{25}

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$2$

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(B) Given $2a = 10 \Rightarrow a = 5$ and $2b = 8 \Rightarrow b = 4$. The eccentricity $e$ is given by $e^2 = 1 - \frac{b^2}{a^2} = 1 - \frac{16}{25} = \frac{9}{25}$,so $e = \frac{3}{5}$. The distance of the focus from the centre is $ae = 5 	imes \frac{3}{5} = 3$. Let the focus be $F(3, 0)$. For a circle centered at $F$ to be tangent to the ellipse and lie entirely within it,the radius $r$ must be the minimum distance from the focus to the ellipse. The distance from a focus to a point on the ellipse is $r = a \pm ex$. The minimum distance occurs at the vertex closest to the focus,which is $x = a$. Thus,$r = a - ae = 5 - 3 = 2$.

An ellipse is drawn with major and minor axes 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 of the circle being outside the ellipse. The radius of the circle is

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