UPSC NDA I and II 2020 Math Solved Paper

Equation of the Ellipse :25x2+16y2=400.

x2

16

+

y2

25

=1
Here a2=16,b2=25
Focci points =(0,±be)=(0,±√b2−a2)
=(0,±√25−16)=(0,±3)
Now, from question point P(x,y) lies on the ellipse, then sum of its distance from two fixed points is always constant, equal to length of its major axis.
Thus, (PQ+PR)=2×5=10.