Question

If you add the lengths of the focal radii of an ellipse, what other value will you produce?

Answer 1

Equation of an ellipse

→having center (0,0) , vertex ($(\pm a ,0)$ and covertex $(\pm b ,0)$ and focus $(\pm c ,0)$ is given by:

$\frac{x^2}{a^2} + \frac{y^2}{b^2}=1$

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 = $F_{1}$

Distance from (-a,0) to (c,0) is = a + c = $F_{2}$

$F_{1} + F_{2} =$ a -c + a +c

          = a + a

        = 2  a  →(Option A )

Answer 2

The figure below shows the representation of this problem. We know from mathematics that an ellipse is a curve in a plane surrounding two focal points called F1 and F2, such that the sum of the distances to the two focal points is constant for every point on the curve. So, for the figure If you add the lengths of the focal radii of an ellipse will produce a constant value equal to 2a that is the line in red.