Equation of an ellipse
→having center (0,0) , vertex ([tex](\pm a ,0)[/tex] and covertex [tex](\pm b ,0)[/tex] and focus [tex](\pm c ,0)[/tex] is given by:
[tex]\frac{x^2}{a^2} + \frac{y^2}{b^2}=1[/tex]
As definition of an ellipse is that locus of all the points in a plane such that it's distance from two fixed points called focii remains constant.
Consider two points (a,0) and (-a,0) on Horizontal axis of an ellipse:
Distance from (a,0) to (c,0) is = a-c = [tex]F_{1}[/tex]
Distance from (-a,0) to (c,0) is = a + c = [tex]F_{2}[/tex]
[tex]F_{1} + F_{2} =[/tex] a -c + a +c
= a + a
= 2 a →(Option A )
