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  4. The latusrectum of the parabola y2=4ax whose focal chord is PSQ such that SP=3 and SQ=2 is given by:

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Q. The latusrectum of the parabola $ {{y}^{2}}=4ax $ whose focal chord is $ PSQ $ such that $ SP=3 $ and $ SQ=2 $ is given by:

Bihar CECEBihar CECE 2006

Solution:

Key Idea : Since the semi-latus rectum of a parabola is the HM of segments of a focal chord.
$\therefore $ Semi-latus rectum $=\frac{2 S P \cdot S Q}{S P+S Q}$
$=\frac{2 \times 3 \times 2}{3+2}=\frac{12}{5}$
$\therefore $ Latus rectum of the parabola $=\frac{24}{5}$.