Question

An ellipse is drawn with major and minor axes of lengths $10$ and $8$ respectively. Using one focus as centre,a circle is drawn that is tangent to the ellipse, with no part of the circle being outside the ellipse. The radiusof the circle is

• A. $\sqrt{3}$
• B. $2$
• C. $2\sqrt{2}$
• D. $\sqrt{5}$

Answer 1

Answer: (B)

$2$

$2a=10,a=5$

$2b=8,b=4$

$b^2=a^2(1-e^2)$

$e^2=1-\frac{16}{25}$

$e=\frac{3}{5}$

Focus of ellipse $(\pm 3,0)$

Taking $(3,0)$ as centre, circle is drawn,

Radius of circle will be $=5-3=2$ units.