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Show that the semi latus rectum of the parabola y^2=4ax is the harmonic mean between segments of any focal chord? Please sir answer fast!

Show that the semi latus rectum of the parabola y^2=4ax is the harmonic mean between segments of any focal chord? Please sir answer fast!

Grade:12th pass

1 Answers

Vikas TU
14149 Points
4 years ago
 If PQ is a Focal Chord of a parabola y² = 4ax, a > 0, 

whose focus is S, then the segments SP and SQ 

of this chord are such that 

... 1/(SP) + 1/(SQ) = 1/a 

∴ 1/(SP) + 1/(SQ) = 2[ 1/(2a) ] 

∴ Harmonic Mean of SP and SQ is 2a ........................................... Ans. : (b) 
. . . . . . . . . . . . . . . . . . . . . . . . . . . .= (1/2)(4a) 
. . . . . . . . . . . . . . . . . . . . . . . . . . . .= (1/2)( Latus Rectum ) 

∴ Harmonic Mean of Segments of a Focal Chord = Semi-Latus-Rectum. 

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