Question

$S$ is one focus of an ellipse and $P$ is any point on the ellipse. If the maximum and minimum values of $SP$ are $m$ and $n$ respectively, then the length of semi major axis is

• A. AM of $m,n$
• B. G.M. of $m,n$
• C. HM of $m,n$
• D. AGP of $m,n$

Answer 1

The correct option is A AM of $m,n$

The minimum and maximum distance between $S$ and $P$ is when $P$ is on the major axis i.e, the vertex of the ellipse.
Let vertex be $A$ and $B$ then $SA=m$ and $SB=n$
Length of semi major axis is $\frac{AB}{2}=\frac{SA+SB}{2}=\frac{m+n}{2}$
Therefore A.M of $m,n$