If PSQ and PS′R are two chords of an ellipse through its  foci S and S respectively, then PSSQ+PS′S′R=

We know that semi latus rectum is harmonic mean of the segments of focal chord.∴ 1SP+1SQ=2ab2----(i) and 1S′P+1S′R=2ab2---(ii) Also SP+S′P=2a----(iii) From (i), 1+SPSQ=2ab2SP From (ii), 1+S′PS′R=2ab2S′P On adding, we get 2+SPSQ+S′PS′R=2ab2SP+S′P⇒ 2+SPSQ+S′PS′R=4a2b2=41−e2⇒ SPSQ+S′PS′R=41−e2−2=21+e21−e2