If PSQ is a focal chord of the ellipse x 2 a 2 - y 2 b 2 -1- a-b- then the harmonic mean of SP and SQ is

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If PSQ is a...

Question

If $P S Q$ is a focal chord of the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1, a > b$ , then the harmonic mean of $S P$ and $S Q$ is

\frac{b^{2}}{a}

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\frac{a^{2}}{b}

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\frac{{2 b}^{2}}{a}

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\frac{{2 a}^{2}}{b}

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Solution

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P S Q

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

a > b

S P

S Q

e

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1 (a > b)

e^{'}

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1 (a < b)

P S Q

\frac{x^{2}}{4} + \frac{y^{2}}{9} = 1

\frac{1}{S P} + \frac{1}{S Q} =

PSQ is a focal chord of the ellipse $\frac{x^{2}}{4} + \frac{y^{2}}{9}$ = 1 then $\frac{1}{S P} + \frac{1}{S Q}$ =

r (< a)

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1, (a > b)

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