First slide

Ellipse

Question

$lf p, q are the segments of a focal chord of an ellipse b^{2} x^{2} + a^{2} y^{2} = a^{2} b^{2}, then$

Moderate

A

$2 b^{2} (p + q) = a p q$
B

$b^{2} (p + q) = 2 a p q$
C

$b^{2} (p + q) = 4 a p q$
D

$4 b^{2} (p + q) = a p q$

Solution

$If P S Q is a focal chord of ellipse then$
$H.M. of S P and S Q is semi latus rectum.$
$\begin{array}{ll} ∴ \frac{1}{S P} + \frac{1}{S Q} = \frac{2 a}{b^{2}} \\ \Rightarrow \frac{1}{p} + \frac{1}{q} = \frac{2 a}{b^{2}} \\ \Rightarrow \frac{p + q}{p q} = \frac{2 a}{b^{2}} \\ \Rightarrow b^{2} (p + q) = 2 a p q \end{array}$

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