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Summary: Trigonometry

The latus rec...

Question

The latus rectum of a parabola whose focal chord is PSQ such that SP=3 and SQ=2 is given by_____

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Solution

$G i v e n S P = 3 S Q = 2 B y p r o p e r t y o f p a r a b o l a T h e h a r m o n i c m e a n o f t h e l e n g t h s t w o p a r t s i n t o w h i c h w h i c h t h e f o c u s d i v i d e s t h e f o c a l c h o r d i s e u a l t o l e n g t h o f s e m i - l a t u s r e c t u m L e t l e n g t h o f l a t u s r e c t u m b e L \frac{2 S P \times S Q}{S P + S Q} = \frac{L}{2} L = \frac{4 \times S P \times S Q}{S P + S Q} = \frac{4 \times 3 \times 2}{3 + 2} = \frac{24}{5}$

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