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The sum of the reciprocals of focal distances of a focal chord $PQ$ of $y^2 = 4ax$ is
The sum of the reciprocals of focal distances of a focal chord $PQ$ of $y^2 = 4ax$ is
Updated On: Apr 17, 2024
- $\frac {1}{a}$
- $a$
- $2a$
- $\frac {1}{2a}$
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The Correct Option is A
Solution and Explanation
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
$=\frac{1}{2 a}+\frac{1}{2 a}=\frac{2}{2 a}=\frac{1}{a}$
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