iran-konkur 2020 Q135

iran-konkur · Other · konkur-riazi_1399_specialized_old-curriculum Conic sections Focal Distance and Point-on-Conic Metric Computation
135- In an ellipse with semi-axes $8$ and $2\sqrt{7}$, and foci $F$ and $F'$, a circle with diameter $F'F$ intersects the ellipse at point $M$. The distance from point $M$ to the nearest focus is:
  • [(1)] $4 - 3\sqrt{2}$
  • [(2)] $7.5$
  • [(3)] $4 - \sqrt{2}$
  • [(4)] $3$
\textbf{135-} In an ellipse with semi-axes $8$ and $2\sqrt{7}$, and foci $F$ and $F'$, a circle with diameter $F'F$ intersects the ellipse at point $M$. The distance from point $M$ to the nearest focus is:

\begin{itemize}
    \item[(1)] $4 - 3\sqrt{2}$
    \item[(2)] $7.5$
    \item[(3)] $4 - \sqrt{2}$
    \item[(4)] $3$
\end{itemize}