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  4. The sum of the reciprocals of focal distances of a focal chord PQ of y2 = 4ax is

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Q. The sum of the reciprocals of focal distances of a focal chord $PQ$ of $y^2 = 4ax$ is

KCETKCET 2011Conic Sections

Solution:

Equation of parabola $y^{2}=4 ax$
Total length of focal chord $=4 a$
and half length of focal chord $=2 a$
Now, sum of the reciprocals of focal distances
$=\frac{1}{2 a}+\frac{1}{2 a}=\frac{2}{2 a}=\frac{1}{a}$