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If the focus of a parabola divides a focal chord of the parabola into segments of lengths 5,3 units, then the length of the latusrectum of that parabola is
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The correct answer is:
$\frac{15}{2}$
Since, semi latusrectum is the harmonic mean of segments.
So, semi laturectum length $=\frac{2 \times 5 \times 3}{5+3}=\frac{30}{8}=\frac{15}{4}$
$\therefore \quad$ Length of latusrectum $=2 \times \frac{15}{4}=\frac{15}{2}$
So, semi laturectum length $=\frac{2 \times 5 \times 3}{5+3}=\frac{30}{8}=\frac{15}{4}$
$\therefore \quad$ Length of latusrectum $=2 \times \frac{15}{4}=\frac{15}{2}$
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