The length of the latus-rectum of the parabola whose focus is ( 2 g u 2 sin 2 α , − 2 g u 2 cos 2 α ) and directrix is y = 2 g u 2 , is

According to the figure, the length of latus rectum is 2 ( SM ) = 2 × 2 g u 2 ( 1 + cos 2 α ) = g 2 u 2 c o s 2 α .

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MathematicsParabolaGeneralMedium2 minPYQ_2011

MathematicsMediumsingle choice

The length of the latus-rectum of the parabola whose focus is $(\frac{u ^{2}}{2 g} sin 2 α, - \frac{u ^{2}}{2 g} cos 2 α)$ and directrix is $y = \frac{u ^{2}}{2 g}$ , is

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Solution:

According to the figure, the length of latus rectum is $2 (SM) = 2 \times \frac{u ^{2}}{2 g} (1 + cos 2 α) = \frac{2 u ^{2} c o s ^{2} α}{g} .$

Stream:BITSATSubject:MathematicsTopic:ParabolaSubtopic:General

⏱ 2mℹ️ Source: PYQ_2011

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