Show that the semi latus rectum of the parabola y^

Question

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!

Vikas TU · Accepted Answer

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.

Analytical Geometry> Show that the semi latus rectum of the pa...

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!

Shuvajyoti Ghosh , 8 Years ago

Vikas TU

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Analytical Geometry> Show that the semi latus rectum of the pa...

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!

Shuvajyoti Ghosh , 8 Years ago

Vikas TU

Provide a better Answer & Earn Cool Goodies

LIVE ONLINE CLASSES

Ask a Doubt

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